Solve 5D^2-7/4=92

$$\frac { 5 D ^ { 2 } - 7 } { 4 } = 92$$

Solve for D

$$D=5\sqrt{3}\approx 8.660254038$$

$$D=-5\sqrt{3}\approx -8.660254038$$

Steps by Finding Square Root

Multiply both sides by 4.

$$5D^{2}-7=92\times 4$$

Multiply 92 and 4 to get 368.

$$5D^{2}-7=368$$

Add 7 to both sides.

$$5D^{2}=368+7$$

Add 368 and 7 to get 375.

$$5D^{2}=375$$

Divide both sides by 5.

$$D^{2}=\frac{375}{5}$$

Divide 375 by 5 to get 75.

$$D^{2}=75$$

Take the square root of both sides of the equation.

$$D=5\sqrt{3} D=-5\sqrt{3}$$

Steps Using the Quadratic Formula

Multiply both sides by 4.

$$5D^{2}-7=92\times 4$$

Multiply 92 and 4 to get 368.

$$5D^{2}-7=368$$

Subtract 368 from both sides.

$$5D^{2}-7-368=0$$

Subtract 368 from -7 to get -375.

$$5D^{2}-375=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and -375 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$D=\frac{0±\sqrt{0^{2}-4\times 5\left(-375\right)}}{2\times 5}$$

Square 0.

$$D=\frac{0±\sqrt{-4\times 5\left(-375\right)}}{2\times 5}$$

Multiply -4 times 5.

$$D=\frac{0±\sqrt{-20\left(-375\right)}}{2\times 5}$$

Multiply -20 times -375.

$$D=\frac{0±\sqrt{7500}}{2\times 5}$$

Take the square root of 7500.

$$D=\frac{0±50\sqrt{3}}{2\times 5}$$

Multiply 2 times 5.

$$D=\frac{0±50\sqrt{3}}{10}$$

Now solve the equation D=\frac{0±50\sqrt{3}}{10} when ± is plus.

$$D=5\sqrt{3}$$

Now solve the equation D=\frac{0±50\sqrt{3}}{10} when ± is minus.

$$D=-5\sqrt{3}$$

The equation is now solved.

$$D=5\sqrt{3} D=-5\sqrt{3}$$