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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+3x^2+15x-3x-15)-90=0

We get rid of parentheses

3x^2+15x-3x-15-90=0

We add all the numbers together, and all the variables

3x^2+12x-105=0

a = 3; b = 12; c = -105;
Δ = b2-4ac
Δ = 122-4·3·(-105)
Δ = 1404
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:

$\sqrt{\Delta}=\sqrt{1404}=\sqrt{36*39}=\sqrt{36}*\sqrt{39}=6\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6\sqrt{39}}{2*3}=\frac{-12-6\sqrt{39}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6\sqrt{39}}{2*3}=\frac{-12+6\sqrt{39}}{6}
$