Solve 6x^2+4=5x^2+9

$$6 x ^ { 2 } + 4 = 5 x ^ { 2 } + 9$$

Solve for x

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

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

Steps by Finding Square Root

Subtract 5x^{2} from both sides.

$$6x^{2}+4-5x^{2}=9$$

Combine 6x^{2} and -5x^{2} to get x^{2}.

$$x^{2}+4=9$$

Subtract 4 from both sides.

$$x^{2}=9-4$$

Subtract 4 from 9 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

Subtract 5x^{2} from both sides.

$$6x^{2}+4-5x^{2}=9$$

Combine 6x^{2} and -5x^{2} to get x^{2}.

$$x^{2}+4=9$$

Subtract 9 from both sides.

$$x^{2}+4-9=0$$

Subtract 9 from 4 to get -5.

$$x^{2}-5=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -5 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Square 0.

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

Multiply -4 times -5.

$$x=\frac{0±\sqrt{20}}{2}$$

Take the square root of 20.

$$x=\frac{0±2\sqrt{5}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{5}}{2} when ± is plus.

$$x=\sqrt{5}$$

Now solve the equation x=\frac{0±2\sqrt{5}}{2} when ± is minus.

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

The equation is now solved.

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