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

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

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

We move all terms to the left:

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

We get rid of parentheses

X^2-2X^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
$