(x-5)=3x^2+3x-90

Solution for (x-5)=3x^2+3x-90 equation:

(x-5)=3x^2+3x-90

We move all terms to the left:

(x-5)-(3x^2+3x-90)=0

We get rid of parentheses

-3x^2+x-3x-5+90=0

We add all the numbers together, and all the variables

-3x^2-2x+85=0

a = -3; b = -2; c = +85;
Δ = b2-4ac
Δ = -22-4·(-3)·85
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-32}{2*-3}=\frac{-30}{-6}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+32}{2*-3}=\frac{34}{-6}
=-5+2/3
$