Solve 8x^2=15left(18-14right)

$$8 { x }^{ 2 } = 15 \left( 18-14 \right)$$

Solve for x

$$x = \frac{\sqrt{30}}{2} \approx 2.738612788$$

$$x = -\frac{\sqrt{30}}{2} \approx -2.738612788$$

Steps by Finding Square Root

Subtract 14 from 18 to get 4.

$$8x^{2}=15\times 4$$

Multiply 15 and 4 to get 60.

$$8x^{2}=60$$

Divide both sides by 8.

$$x^{2}=\frac{60}{8}$$

Reduce the fraction \frac{60}{8} to lowest terms by extracting and canceling out 4.

$$x^{2}=\frac{15}{2}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{30}}{2} x=-\frac{\sqrt{30}}{2}$$

Steps Using the Quadratic Formula

Subtract 14 from 18 to get 4.

$$8x^{2}=15\times 4$$

Multiply 15 and 4 to get 60.

$$8x^{2}=60$$

Subtract 60 from both sides.

$$8x^{2}-60=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 8 for a, 0 for b, and -60 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 8\left(-60\right)}}{2\times 8}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 8\left(-60\right)}}{2\times 8}$$

Multiply -4 times 8.

$$x=\frac{0±\sqrt{-32\left(-60\right)}}{2\times 8}$$

Multiply -32 times -60.

$$x=\frac{0±\sqrt{1920}}{2\times 8}$$

Take the square root of 1920.

$$x=\frac{0±8\sqrt{30}}{2\times 8}$$

Multiply 2 times 8.

$$x=\frac{0±8\sqrt{30}}{16}$$

Now solve the equation x=\frac{0±8\sqrt{30}}{16} when ± is plus.

$$x=\frac{\sqrt{30}}{2}$$

Now solve the equation x=\frac{0±8\sqrt{30}}{16} when ± is minus.

$$x=-\frac{\sqrt{30}}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{30}}{2} x=-\frac{\sqrt{30}}{2}$$