(5x+2)(2x-8)=39

Solution for (5x+2)(2x-8)=39 equation:

(5x+2)(2x-8)=39

We move all terms to the left:

(5x+2)(2x-8)-(39)=0

We multiply parentheses ..

(+10x^2-40x+4x-16)-39=0

We get rid of parentheses

10x^2-40x+4x-16-39=0

We add all the numbers together, and all the variables

10x^2-36x-55=0

a = 10; b = -36; c = -55;
Δ = b2-4ac
Δ = -362-4·10·(-55)
Δ = 3496
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:

$\sqrt{\Delta}=\sqrt{3496}=\sqrt{4*874}=\sqrt{4}*\sqrt{874}=2\sqrt{874}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-2\sqrt{874}}{2*10}=\frac{36-2\sqrt{874}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+2\sqrt{874}}{2*10}=\frac{36+2\sqrt{874}}{20}
$