(2x-10)(x+30)=110

Solution for (2x-10)(x+30)=110 equation:

(2x-10)(x+30)=110

We move all terms to the left:

(2x-10)(x+30)-(110)=0

We multiply parentheses ..

(+2x^2+60x-10x-300)-110=0

We get rid of parentheses

2x^2+60x-10x-300-110=0

We add all the numbers together, and all the variables

2x^2+50x-410=0

a = 2; b = 50; c = -410;
Δ = b2-4ac
Δ = 502-4·2·(-410)
Δ = 5780
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:

$\sqrt{\Delta}=\sqrt{5780}=\sqrt{1156*5}=\sqrt{1156}*\sqrt{5}=34\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-34\sqrt{5}}{2*2}=\frac{-50-34\sqrt{5}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+34\sqrt{5}}{2*2}=\frac{-50+34\sqrt{5}}{4}
$