Solve 5x^2+6=20

$$5 x ^ { 2 } + 6 = 20$$

Solve for x

$$x = \frac{\sqrt{70}}{5} \approx 1.673320053$$

$$x = -\frac{\sqrt{70}}{5} \approx -1.673320053$$

Steps by Finding Square Root

Subtract 6 from both sides.

$$5x^{2}=20-6$$

Subtract 6 from 20 to get 14.

$$5x^{2}=14$$

Divide both sides by 5.

$$x^{2}=\frac{14}{5}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{70}}{5} x=-\frac{\sqrt{70}}{5}$$

Steps Using the Quadratic Formula

Subtract 20 from both sides.

$$5x^{2}+6-20=0$$

Subtract 20 from 6 to get -14.

$$5x^{2}-14=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and -14 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 5\left(-14\right)}}{2\times 5}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 5\left(-14\right)}}{2\times 5}$$

Multiply -4 times 5.

$$x=\frac{0±\sqrt{-20\left(-14\right)}}{2\times 5}$$

Multiply -20 times -14.

$$x=\frac{0±\sqrt{280}}{2\times 5}$$

Take the square root of 280.

$$x=\frac{0±2\sqrt{70}}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{0±2\sqrt{70}}{10}$$

Now solve the equation x=\frac{0±2\sqrt{70}}{10} when ± is plus.

$$x=\frac{\sqrt{70}}{5}$$

Now solve the equation x=\frac{0±2\sqrt{70}}{10} when ± is minus.

$$x=-\frac{\sqrt{70}}{5}$$

The equation is now solved.

$$x=\frac{\sqrt{70}}{5} x=-\frac{\sqrt{70}}{5}$$