(x-35)(x-25)=300

Solution for (x-35)(x-25)=300 equation:

(x-35)(x-25)=300

We move all terms to the left:

(x-35)(x-25)-(300)=0

We multiply parentheses ..

(+x^2-25x-35x+875)-300=0

We get rid of parentheses

x^2-25x-35x+875-300=0

We add all the numbers together, and all the variables

x^2-60x+575=0

a = 1; b = -60; c = +575;
Δ = b2-4ac
Δ = -602-4·1·575
Δ = 1300
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:

$\sqrt{\Delta}=\sqrt{1300}=\sqrt{100*13}=\sqrt{100}*\sqrt{13}=10\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-10\sqrt{13}}{2*1}=\frac{60-10\sqrt{13}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+10\sqrt{13}}{2*1}=\frac{60+10\sqrt{13}}{2}
$