52=(2x+6)(x-8)

Solution for 52=(2x+6)(x-8) equation:

52=(2x+6)(x-8)

We move all terms to the left:

52-((2x+6)(x-8))=0

We multiply parentheses ..

-((+2x^2-16x+6x-48))+52=0


We calculate terms in parentheses: -((+2x^2-16x+6x-48)), so:

(+2x^2-16x+6x-48)

We get rid of parentheses

2x^2-16x+6x-48

We add all the numbers together, and all the variables

2x^2-10x-48

Back to the equation:

-(2x^2-10x-48)


We get rid of parentheses

-2x^2+10x+48+52=0

We add all the numbers together, and all the variables

-2x^2+10x+100=0

a = -2; b = 10; c = +100;
Δ = b2-4ac
Δ = 102-4·(-2)·100
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-30}{2*-2}=\frac{-40}{-4}
=+10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+30}{2*-2}=\frac{20}{-4}
=-5
$