(2x-10)(x-20)=25

Solution for (2x-10)(x-20)=25 equation:

(2x-10)(x-20)=25

We move all terms to the left:

(2x-10)(x-20)-(25)=0

We multiply parentheses ..

(+2x^2-40x-10x+200)-25=0

We get rid of parentheses

2x^2-40x-10x+200-25=0

We add all the numbers together, and all the variables

2x^2-50x+175=0

a = 2; b = -50; c = +175;
Δ = b2-4ac
Δ = -502-4·2·175
Δ = 1100
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:

$\sqrt{\Delta}=\sqrt{1100}=\sqrt{100*11}=\sqrt{100}*\sqrt{11}=10\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-10\sqrt{11}}{2*2}=\frac{50-10\sqrt{11}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+10\sqrt{11}}{2*2}=\frac{50+10\sqrt{11}}{4}
$