(5x)(x-5)+(5x-3)(x-6)=0

Solution for (5x)(x-5)+(5x-3)(x-6)=0 equation:

(5x)(x-5)+(5x-3)(x-6)=0

We multiply parentheses

5x^2-25x+(5x-3)(x-6)=0

We multiply parentheses ..

5x^2+(+5x^2-30x-3x+18)-25x=0

We get rid of parentheses

5x^2+5x^2-30x-3x-25x+18=0

We add all the numbers together, and all the variables

10x^2-58x+18=0

a = 10; b = -58; c = +18;
Δ = b2-4ac
Δ = -582-4·10·18
Δ = 2644
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:

$\sqrt{\Delta}=\sqrt{2644}=\sqrt{4*661}=\sqrt{4}*\sqrt{661}=2\sqrt{661}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-58)-2\sqrt{661}}{2*10}=\frac{58-2\sqrt{661}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-58)+2\sqrt{661}}{2*10}=\frac{58+2\sqrt{661}}{20}
$