(3x-3)(x-7)=90

Solution for (3x-3)(x-7)=90 equation:

(3x-3)(x-7)=90

We move all terms to the left:

(3x-3)(x-7)-(90)=0

We multiply parentheses ..

(+3x^2-21x-3x+21)-90=0

We get rid of parentheses

3x^2-21x-3x+21-90=0

We add all the numbers together, and all the variables

3x^2-24x-69=0

a = 3; b = -24; c = -69;
Δ = b2-4ac
Δ = -242-4·3·(-69)
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{-(-24)-6\sqrt{39}}{2*3}=\frac{24-6\sqrt{39}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+6\sqrt{39}}{2*3}=\frac{24+6\sqrt{39}}{6}
$