-x^2+3x=4x-12

Solution for -x^2+3x=4x-12 equation:

-x^2+3x=4x-12

We move all terms to the left:

-x^2+3x-(4x-12)=0

We add all the numbers together, and all the variables

-1x^2+3x-(4x-12)=0

We get rid of parentheses

-1x^2+3x-4x+12=0

We add all the numbers together, and all the variables

-1x^2-1x+12=0

a = -1; b = -1; c = +12;
Δ = b2-4ac
Δ = -12-4·(-1)·12
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-7}{2*-1}=\frac{-6}{-2}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+7}{2*-1}=\frac{8}{-2}
=-4
$