Solve 5n^2-7=128

$$5 n ^ { 2 } - 7 = 128$$

Solve for n

$$n=3\sqrt{3}\approx 5.196152423$$

$$n=-3\sqrt{3}\approx -5.196152423$$

Steps by Finding Square Root

Add 7 to both sides.

$$5n^{2}=128+7$$

Add 128 and 7 to get 135.

$$5n^{2}=135$$

Divide both sides by 5.

$$n^{2}=\frac{135}{5}$$

Divide 135 by 5 to get 27.

$$n^{2}=27$$

Take the square root of both sides of the equation.

$$n=3\sqrt{3} n=-3\sqrt{3}$$

Steps Using the Quadratic Formula

Subtract 128 from both sides.

$$5n^{2}-7-128=0$$

Subtract 128 from -7 to get -135.

$$5n^{2}-135=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and -135 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$n=\frac{0±\sqrt{0^{2}-4\times 5\left(-135\right)}}{2\times 5}$$

Square 0.

$$n=\frac{0±\sqrt{-4\times 5\left(-135\right)}}{2\times 5}$$

Multiply -4 times 5.

$$n=\frac{0±\sqrt{-20\left(-135\right)}}{2\times 5}$$

Multiply -20 times -135.

$$n=\frac{0±\sqrt{2700}}{2\times 5}$$

Take the square root of 2700.

$$n=\frac{0±30\sqrt{3}}{2\times 5}$$

Multiply 2 times 5.

$$n=\frac{0±30\sqrt{3}}{10}$$

Now solve the equation n=\frac{0±30\sqrt{3}}{10} when ± is plus.

$$n=3\sqrt{3}$$

Now solve the equation n=\frac{0±30\sqrt{3}}{10} when ± is minus.

$$n=-3\sqrt{3}$$

The equation is now solved.

$$n=3\sqrt{3} n=-3\sqrt{3}$$