Solve 36+4x^2-121/12x=36+x^2-49/12x

$$\frac{ 36+4 { x }^{ 2 } -121 }{ 12x } = \frac{ 36+ { x }^{ 2 } -49 }{ 12x }$$

Solve for x

$$x=2\sqrt{6}\approx 4.898979486$$

$$x=-2\sqrt{6}\approx -4.898979486$$

Steps by Finding Square Root

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 12x.

$$36+4x^{2}-121=36+x^{2}-49$$

Subtract 121 from 36 to get -85.

$$-85+4x^{2}=36+x^{2}-49$$

Subtract 49 from 36 to get -13.

$$-85+4x^{2}=-13+x^{2}$$

Subtract x^{2} from both sides.

$$-85+4x^{2}-x^{2}=-13$$

Combine 4x^{2} and -x^{2} to get 3x^{2}.

$$-85+3x^{2}=-13$$

Add 85 to both sides.

$$3x^{2}=-13+85$$

Add -13 and 85 to get 72.

$$3x^{2}=72$$

Divide both sides by 3.

$$x^{2}=\frac{72}{3}$$

Divide 72 by 3 to get 24.

$$x^{2}=24$$

Take the square root of both sides of the equation.

$$x=2\sqrt{6} x=-2\sqrt{6}$$

Steps Using the Quadratic Formula

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 12x.

$$36+4x^{2}-121=36+x^{2}-49$$

Subtract 121 from 36 to get -85.

$$-85+4x^{2}=36+x^{2}-49$$

Subtract 49 from 36 to get -13.

$$-85+4x^{2}=-13+x^{2}$$

Subtract -13 from both sides.

$$-85+4x^{2}-\left(-13\right)=x^{2}$$

The opposite of -13 is 13.

$$-85+4x^{2}+13=x^{2}$$

Subtract x^{2} from both sides.

$$-85+4x^{2}+13-x^{2}=0$$

Add -85 and 13 to get -72.

$$-72+4x^{2}-x^{2}=0$$

Combine 4x^{2} and -x^{2} to get 3x^{2}.

$$-72+3x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$3x^{2}-72=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -72 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-72\right)}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-72\right)}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\left(-72\right)}}{2\times 3}$$

Multiply -12 times -72.

$$x=\frac{0±\sqrt{864}}{2\times 3}$$

Take the square root of 864.

$$x=\frac{0±12\sqrt{6}}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±12\sqrt{6}}{6}$$

Now solve the equation x=\frac{0±12\sqrt{6}}{6} when ± is plus.

$$x=2\sqrt{6}$$

Now solve the equation x=\frac{0±12\sqrt{6}}{6} when ± is minus.

$$x=-2\sqrt{6}$$

The equation is now solved.

$$x=2\sqrt{6} x=-2\sqrt{6}$$