Solve 12x^2+3x(x-3x)+9=90

$$12 { x }^{ 2 } +3x(x-3x)+9=90$$

Solve for x

$$x = \frac{3 \sqrt{6}}{2} \approx 3.674234614$$

$$x = -\frac{3 \sqrt{6}}{2} \approx -3.674234614$$

Steps by Finding Square Root

Combine x and -3x to get -2x.

$$12x^{2}+3x\left(-2\right)x+9=90$$

Multiply 3 and -2 to get -6.

$$12x^{2}-6xx+9=90$$

Multiply x and x to get x^{2}.

$$12x^{2}-6x^{2}+9=90$$

Combine 12x^{2} and -6x^{2} to get 6x^{2}.

$$6x^{2}+9=90$$

Subtract 9 from both sides.

$$6x^{2}=90-9$$

Subtract 9 from 90 to get 81.

$$6x^{2}=81$$

Divide both sides by 6.

$$x^{2}=\frac{81}{6}$$

Reduce the fraction \frac{81}{6} to lowest terms by extracting and canceling out 3.

$$x^{2}=\frac{27}{2}$$

Take the square root of both sides of the equation.

$$x=\frac{3\sqrt{6}}{2} x=-\frac{3\sqrt{6}}{2}$$

Steps Using the Quadratic Formula

Combine x and -3x to get -2x.

$$12x^{2}+3x\left(-2\right)x+9=90$$

Multiply 3 and -2 to get -6.

$$12x^{2}-6xx+9=90$$

Multiply x and x to get x^{2}.

$$12x^{2}-6x^{2}+9=90$$

Combine 12x^{2} and -6x^{2} to get 6x^{2}.

$$6x^{2}+9=90$$

Subtract 90 from both sides.

$$6x^{2}+9-90=0$$

Subtract 90 from 9 to get -81.

$$6x^{2}-81=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 6 for a, 0 for b, and -81 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 6\left(-81\right)}}{2\times 6}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 6\left(-81\right)}}{2\times 6}$$

Multiply -4 times 6.

$$x=\frac{0±\sqrt{-24\left(-81\right)}}{2\times 6}$$

Multiply -24 times -81.

$$x=\frac{0±\sqrt{1944}}{2\times 6}$$

Take the square root of 1944.

$$x=\frac{0±18\sqrt{6}}{2\times 6}$$

Multiply 2 times 6.

$$x=\frac{0±18\sqrt{6}}{12}$$

Now solve the equation x=\frac{0±18\sqrt{6}}{12} when ± is plus.

$$x=\frac{3\sqrt{6}}{2}$$

Now solve the equation x=\frac{0±18\sqrt{6}}{12} when ± is minus.

$$x=-\frac{3\sqrt{6}}{2}$$

The equation is now solved.

$$x=\frac{3\sqrt{6}}{2} x=-\frac{3\sqrt{6}}{2}$$