(10x+525)(10x+509)=13

Solution for (10x+525)(10x+509)=13 equation:

(10x+525)(10x+509)=13

We move all terms to the left:

(10x+525)(10x+509)-(13)=0

We multiply parentheses ..

(+100x^2+5090x+5250x+267225)-13=0

We get rid of parentheses

100x^2+5090x+5250x+267225-13=0

We add all the numbers together, and all the variables

100x^2+10340x+267212=0

a = 100; b = 10340; c = +267212;
Δ = b2-4ac
Δ = 103402-4·100·267212
Δ = 30800
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:

$\sqrt{\Delta}=\sqrt{30800}=\sqrt{400*77}=\sqrt{400}*\sqrt{77}=20\sqrt{77}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10340)-20\sqrt{77}}{2*100}=\frac{-10340-20\sqrt{77}}{200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10340)+20\sqrt{77}}{2*100}=\frac{-10340+20\sqrt{77}}{200}
$