X2+3x=12-2x-X2

Solution for X2+3x=12-2x-X2 equation:

X2+3X=12-2X-X2

We move all terms to the left:

X2+3X-(12-2X-X2)=0

We add all the numbers together, and all the variables

-(-2X-1X^2+12)+X2+3X=0

We add all the numbers together, and all the variables

X^2-(-2X-1X^2+12)+3X=0

We get rid of parentheses

X^2+1X^2+2X+3X-12=0

We add all the numbers together, and all the variables

2X^2+5X-12=0

a = 2; b = 5; c = -12;
Δ = b2-4ac
Δ = 52-4·2·(-12)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-11}{2*2}=\frac{-16}{4}
=-4
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+11}{2*2}=\frac{6}{4}
=1+1/2
$