(2x-11)(x-6)=666

Solution for (2x-11)(x-6)=666 equation:

(2x-11)(x-6)=666

We move all terms to the left:

(2x-11)(x-6)-(666)=0

We multiply parentheses ..

(+2x^2-12x-11x+66)-666=0

We get rid of parentheses

2x^2-12x-11x+66-666=0

We add all the numbers together, and all the variables

2x^2-23x-600=0

a = 2; b = -23; c = -600;
Δ = b2-4ac
Δ = -232-4·2·(-600)
Δ = 5329
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5329}=73$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-73}{2*2}=\frac{-50}{4}
=-12+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+73}{2*2}=\frac{96}{4}
=24
$