4x-x(x-3)=-6+5x-12

Solution for 4x-x(x-3)=-6+5x-12 equation:

4x-x(x-3)=-6+5x-12

We move all terms to the left:

4x-x(x-3)-(-6+5x-12)=0

We add all the numbers together, and all the variables

4x-x(x-3)-(5x-18)=0

We multiply parentheses

-x^2+4x+3x-(5x-18)=0

We get rid of parentheses

-x^2+4x+3x-5x+18=0

We add all the numbers together, and all the variables

-1x^2+2x+18=0

a = -1; b = 2; c = +18;
Δ = b2-4ac
Δ = 22-4·(-1)·18
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{19}}{2*-1}=\frac{-2-2\sqrt{19}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{19}}{2*-1}=\frac{-2+2\sqrt{19}}{-2}
$