Solve 5D^2/4+7=92

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

Solve for D

$$D=2\sqrt{17}\approx 8.246211251$$

$$D=-2\sqrt{17}\approx -8.246211251$$

Steps by Finding Square Root

Multiply both sides of the equation by 4.

$$5D^{2}+28=368$$

Subtract 28 from both sides.

$$5D^{2}=368-28$$

Subtract 28 from 368 to get 340.

$$5D^{2}=340$$

Divide both sides by 5.

$$D^{2}=\frac{340}{5}$$

Divide 340 by 5 to get 68.

$$D^{2}=68$$

Take the square root of both sides of the equation.

$$D=2\sqrt{17} D=-2\sqrt{17}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 4.

$$5D^{2}+28=368$$

Subtract 368 from both sides.

$$5D^{2}+28-368=0$$

Subtract 368 from 28 to get -340.

$$5D^{2}-340=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and -340 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$D=\frac{0±\sqrt{0^{2}-4\times 5\left(-340\right)}}{2\times 5}$$

Square 0.

$$D=\frac{0±\sqrt{-4\times 5\left(-340\right)}}{2\times 5}$$

Multiply -4 times 5.

$$D=\frac{0±\sqrt{-20\left(-340\right)}}{2\times 5}$$

Multiply -20 times -340.

$$D=\frac{0±\sqrt{6800}}{2\times 5}$$

Take the square root of 6800.

$$D=\frac{0±20\sqrt{17}}{2\times 5}$$

Multiply 2 times 5.

$$D=\frac{0±20\sqrt{17}}{10}$$

Now solve the equation D=\frac{0±20\sqrt{17}}{10} when ± is plus.

$$D=2\sqrt{17}$$

Now solve the equation D=\frac{0±20\sqrt{17}}{10} when ± is minus.

$$D=-2\sqrt{17}$$

The equation is now solved.

$$D=2\sqrt{17} D=-2\sqrt{17}$$