(X-6)=3x^2+3x-90

Solution for (X-6)=3x^2+3x-90 equation:

(X-6)=3X^2+3X-90

We move all terms to the left:

(X-6)-(3X^2+3X-90)=0

We get rid of parentheses

-3X^2+X-3X-6+90=0

We add all the numbers together, and all the variables

-3X^2-2X+84=0

a = -3; b = -2; c = +84;
Δ = b2-4ac
Δ = -22-4·(-3)·84
Δ = 1012
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1012}=\sqrt{4*253}=\sqrt{4}*\sqrt{253}=2\sqrt{253}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{253}}{2*-3}=\frac{2-2\sqrt{253}}{-6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{253}}{2*-3}=\frac{2+2\sqrt{253}}{-6}
$