Solve 5x^2-3=150

$$5 { x }^{ 2 } -3=150$$

Solve for x

$$x = \frac{3 \sqrt{85}}{5} \approx 5.531726674$$

$$x = -\frac{3 \sqrt{85}}{5} \approx -5.531726674$$

Steps by Finding Square Root

Add 3 to both sides.

$$5x^{2}=150+3$$

Add 150 and 3 to get 153.

$$5x^{2}=153$$

Divide both sides by 5.

$$x^{2}=\frac{153}{5}$$

Take the square root of both sides of the equation.

$$x=\frac{3\sqrt{85}}{5} x=-\frac{3\sqrt{85}}{5}$$

Steps Using the Quadratic Formula

Subtract 150 from both sides.

$$5x^{2}-3-150=0$$

Subtract 150 from -3 to get -153.

$$5x^{2}-153=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and -153 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 5\left(-153\right)}}{2\times 5}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 5\left(-153\right)}}{2\times 5}$$

Multiply -4 times 5.

$$x=\frac{0±\sqrt{-20\left(-153\right)}}{2\times 5}$$

Multiply -20 times -153.

$$x=\frac{0±\sqrt{3060}}{2\times 5}$$

Take the square root of 3060.

$$x=\frac{0±6\sqrt{85}}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{0±6\sqrt{85}}{10}$$

Now solve the equation x=\frac{0±6\sqrt{85}}{10} when ± is plus.

$$x=\frac{3\sqrt{85}}{5}$$

Now solve the equation x=\frac{0±6\sqrt{85}}{10} when ± is minus.

$$x=-\frac{3\sqrt{85}}{5}$$

The equation is now solved.

$$x=\frac{3\sqrt{85}}{5} x=-\frac{3\sqrt{85}}{5}$$