(2x+5)(x-10)=80

Solution for (2x+5)(x-10)=80 equation:

(2x+5)(x-10)=80

We move all terms to the left:

(2x+5)(x-10)-(80)=0

We multiply parentheses ..

(+2x^2-20x+5x-50)-80=0

We get rid of parentheses

2x^2-20x+5x-50-80=0

We add all the numbers together, and all the variables

2x^2-15x-130=0

a = 2; b = -15; c = -130;
Δ = b2-4ac
Δ = -152-4·2·(-130)
Δ = 1265
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{1265}}{2*2}=\frac{15-\sqrt{1265}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{1265}}{2*2}=\frac{15+\sqrt{1265}}{4}
$