X^2+5x-12=-2x^2-3x+7

Solution for X^2+5x-12=-2x^2-3x+7 equation:

X^2+5X-12=-2X^2-3X+7

We move all terms to the left:

X^2+5X-12-(-2X^2-3X+7)=0

We get rid of parentheses

X^2+2X^2+3X+5X-7-12=0

We add all the numbers together, and all the variables

3X^2+8X-19=0

a = 3; b = 8; c = -19;
Δ = b2-4ac
Δ = 82-4·3·(-19)
Δ = 292
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:

$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{73}}{2*3}=\frac{-8-2\sqrt{73}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{73}}{2*3}=\frac{-8+2\sqrt{73}}{6}
$