(x+7)(3x-6)=66

Solution for (x+7)(3x-6)=66 equation:

(x+7)(3x-6)=66

We move all terms to the left:

(x+7)(3x-6)-(66)=0

We multiply parentheses ..

(+3x^2-6x+21x-42)-66=0

We get rid of parentheses

3x^2-6x+21x-42-66=0

We add all the numbers together, and all the variables

3x^2+15x-108=0

a = 3; b = 15; c = -108;
Δ = b2-4ac
Δ = 152-4·3·(-108)
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-39}{2*3}=\frac{-54}{6}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+39}{2*3}=\frac{24}{6}
=4
$