Solve 5x^2-3=75

$$5 x ^ { 2 } - 3 = 75$$

Solve for x

$$x = \frac{\sqrt{390}}{5} \approx 3.949683532$$

$$x = -\frac{\sqrt{390}}{5} \approx -3.949683532$$

Steps by Finding Square Root

Add 3 to both sides.

$$5x^{2}=75+3$$

Add 75 and 3 to get 78.

$$5x^{2}=78$$

Divide both sides by 5.

$$x^{2}=\frac{78}{5}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{390}}{5} x=-\frac{\sqrt{390}}{5}$$

Steps Using the Quadratic Formula

Subtract 75 from both sides.

$$5x^{2}-3-75=0$$

Subtract 75 from -3 to get -78.

$$5x^{2}-78=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and -78 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 5\left(-78\right)}}{2\times 5}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 5\left(-78\right)}}{2\times 5}$$

Multiply -4 times 5.

$$x=\frac{0±\sqrt{-20\left(-78\right)}}{2\times 5}$$

Multiply -20 times -78.

$$x=\frac{0±\sqrt{1560}}{2\times 5}$$

Take the square root of 1560.

$$x=\frac{0±2\sqrt{390}}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{0±2\sqrt{390}}{10}$$

Now solve the equation x=\frac{0±2\sqrt{390}}{10} when ± is plus.

$$x=\frac{\sqrt{390}}{5}$$

Now solve the equation x=\frac{0±2\sqrt{390}}{10} when ± is minus.

$$x=-\frac{\sqrt{390}}{5}$$

The equation is now solved.

$$x=\frac{\sqrt{390}}{5} x=-\frac{\sqrt{390}}{5}$$