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Solve 5x² - 12 = 0

The solutions of 5x² - 12 = 0 are x = (2√15)/5 or x = (-2√15)/5, that is x ≈ 1.5491933 and x ≈ -1.5491933.

x² +x += 0
5x2−12=0⇒x=2155, −21555x^2 - 12 = 0 \Rightarrow x = \frac{2\sqrt{15}}{5},\ \frac{-2\sqrt{15}}{5}
Discriminant D = 240 · x ≈ 1.54919, -1.54919

Change a, b or c (whole numbers, a not 0) and the exact solutions follow.

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Graph of y = 5x² - 12-4-3-2-11234-20204060x = 1.5491933x = -1.5491933vertexy = 5x² - 12
Graph of y = 5x² - 12. The curve crosses the x-axis at x = 1.5491933 and x = -1.5491933; the vertex is at (0, -12).

How to work it out

  1. 1

    Write it in standard form a x² + b x + c = 0 and read off the coefficients: a = 5, b = 0, c = -12.

    5x2−12=05x^2 - 12 = 0
  2. 2

    Work out the discriminant D = b² − 4ac. Its sign tells you how many real solutions there are.

    D=02−4⋅5⋅(−12)=0+240=240D = 0^2 - 4\cdot5\cdot(-12) = 0 + 240 = 240
  3. 3

    D is positive, so there are two different real solutions.

  4. 4

    The quadratic formula works for every quadratic:

    x=−b±D2a=0±24010x = \frac{-b \pm \sqrt{D}}{2a} = \frac{0 \pm \sqrt{240}}{10}
  5. 5

    Simplify (pull the square out of the root) to get the solutions:

    x=2155orx=−2155x = \frac{2\sqrt{15}}{5}\quad\text{or}\quad x = \frac{-2\sqrt{15}}{5}
  6. 6

    As decimals: x ≈ 1.5491933 and x ≈ -1.5491933.

  7. 7

    Check numerically: for x ≈ 1.5491933 the left side is 0 (zero up to rounding) ✓

LaTeX source of the formulas on this page
\[ 5x^2 - 12 = 0\ \Rightarrow\ x = \frac{2\sqrt{15}}{5},\ \frac{-2\sqrt{15}}{5} \]
\[ 5x^2 - 12 = 0 \]
\[ D = 0^2 - 4\cdot5\cdot(-12) = 0 + 240 = 240 \]
\[ x = \frac{-b \pm \sqrt{D}}{2a} = \frac{0 \pm \sqrt{240}}{10} \]
\[ x = \frac{2\sqrt{15}}{5}\quad\text{or}\quad x = \frac{-2\sqrt{15}}{5} \]

The parabola y = 5x² - 12

xy
-333
-28
-1-7
0-12
1-7
28
333

Questions

What are the solutions of 5x² - 12 = 0?

The solutions of 5x² - 12 = 0 are x = (2√15)/5 or x = (-2√15)/5, that is x ≈ 1.5491933 and x ≈ -1.5491933.

Does 5x² - 12 = 0 factor?

Not over the integers, because the discriminant 240 is not a perfect square. Use the quadratic formula.

What is the vertex of y = 5x² - 12?

(0, -12). The parabola opens upwards, so this is the minimum.

What are the sum and product of the roots?

Sum = −b/a = 0, product = c/a = -12/5.

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    Solve 5x² - 12 = 0: x = (2√15)/5 or x = (-2√15)/5 (steps) | WordGPT