3x-5x(x-5)=-2+3+12

Solution for 3x-5x(x-5)=-2+3+12 equation:

3x-5x(x-5)=-2+3+12

We move all terms to the left:

3x-5x(x-5)-(-2+3+12)=0

We add all the numbers together, and all the variables

3x-5x(x-5)-13=0

We multiply parentheses

-5x^2+3x+25x-13=0

We add all the numbers together, and all the variables

-5x^2+28x-13=0

a = -5; b = 28; c = -13;
Δ = b2-4ac
Δ = 282-4·(-5)·(-13)
Δ = 524
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:

$\sqrt{\Delta}=\sqrt{524}=\sqrt{4*131}=\sqrt{4}*\sqrt{131}=2\sqrt{131}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-2\sqrt{131}}{2*-5}=\frac{-28-2\sqrt{131}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+2\sqrt{131}}{2*-5}=\frac{-28+2\sqrt{131}}{-10}
$