Solve 56/x^2+3=7

$$\frac { 56 } { x ^ { 2 } + 3 } = 7$$

Solve for x

$$x=\sqrt{5}\approx 2.236067977$$

$$x=-\sqrt{5}\approx -2.236067977$$

Steps by Finding Square Root

Multiply both sides of the equation by x^{2}+3.

$$56=7\left(x^{2}+3\right)$$

Use the distributive property to multiply 7 by x^{2}+3.

$$56=7x^{2}+21$$

Swap sides so that all variable terms are on the left hand side.

$$7x^{2}+21=56$$

Subtract 21 from both sides.

$$7x^{2}=56-21$$

Subtract 21 from 56 to get 35.

$$7x^{2}=35$$

Divide both sides by 7.

$$x^{2}=\frac{35}{7}$$

Divide 35 by 7 to get 5.

$$x^{2}=5$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Multiply both sides of the equation by x^{2}+3.

$$56=7\left(x^{2}+3\right)$$

Use the distributive property to multiply 7 by x^{2}+3.

$$56=7x^{2}+21$$

Swap sides so that all variable terms are on the left hand side.

$$7x^{2}+21=56$$

Subtract 56 from both sides.

$$7x^{2}+21-56=0$$

Subtract 56 from 21 to get -35.

$$7x^{2}-35=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 7 for a, 0 for b, and -35 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 7\left(-35\right)}}{2\times 7}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 7\left(-35\right)}}{2\times 7}$$

Multiply -4 times 7.

$$x=\frac{0±\sqrt{-28\left(-35\right)}}{2\times 7}$$

Multiply -28 times -35.

$$x=\frac{0±\sqrt{980}}{2\times 7}$$

Take the square root of 980.

$$x=\frac{0±14\sqrt{5}}{2\times 7}$$

Multiply 2 times 7.

$$x=\frac{0±14\sqrt{5}}{14}$$

Now solve the equation x=\frac{0±14\sqrt{5}}{14} when ± is plus.

$$x=\sqrt{5}$$

Now solve the equation x=\frac{0±14\sqrt{5}}{14} when ± is minus.

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

The equation is now solved.

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