12x-5x(x-5)=7x+5

Solution for 12x-5x(x-5)=7x+5 equation:

12x-5x(x-5)=7x+5

We move all terms to the left:

12x-5x(x-5)-(7x+5)=0

We multiply parentheses

-5x^2+12x+25x-(7x+5)=0

We get rid of parentheses

-5x^2+12x+25x-7x-5=0

We add all the numbers together, and all the variables

-5x^2+30x-5=0

a = -5; b = 30; c = -5;
Δ = b2-4ac
Δ = 302-4·(-5)·(-5)
Δ = 800
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:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-20\sqrt{2}}{2*-5}=\frac{-30-20\sqrt{2}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+20\sqrt{2}}{2*-5}=\frac{-30+20\sqrt{2}}{-10}
$