(2x-4)(x+8)=66

Solution for (2x-4)(x+8)=66 equation:

(2x-4)(x+8)=66

We move all terms to the left:

(2x-4)(x+8)-(66)=0

We multiply parentheses ..

(+2x^2+16x-4x-32)-66=0

We get rid of parentheses

2x^2+16x-4x-32-66=0

We add all the numbers together, and all the variables

2x^2+12x-98=0

a = 2; b = 12; c = -98;
Δ = b2-4ac
Δ = 122-4·2·(-98)
Δ = 928
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:

$\sqrt{\Delta}=\sqrt{928}=\sqrt{16*58}=\sqrt{16}*\sqrt{58}=4\sqrt{58}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{58}}{2*2}=\frac{-12-4\sqrt{58}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{58}}{2*2}=\frac{-12+4\sqrt{58}}{4}
$