4x-3x(x-5)=x

Solution for 4x-3x(x-5)=x equation:

4x-3x(x-5)=x

We move all terms to the left:

4x-3x(x-5)-(x)=0

We add all the numbers together, and all the variables

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

We multiply parentheses

-3x^2+3x+15x=0

We add all the numbers together, and all the variables

-3x^2+18x=0

a = -3; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·(-3)·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*-3}=\frac{-36}{-6}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*-3}=\frac{0}{-6}
=0
$