X^2+2x-15=2x^2-5x-12

Solution for X^2+2x-15=2x^2-5x-12 equation:

X^2+2X-15=2X^2-5X-12

We move all terms to the left:

X^2+2X-15-(2X^2-5X-12)=0

We get rid of parentheses

X^2-2X^2+2X+5X+12-15=0

We add all the numbers together, and all the variables

-1X^2+7X-3=0

a = -1; b = 7; c = -3;
Δ = b2-4ac
Δ = 72-4·(-1)·(-3)
Δ = 37
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{37}}{2*-1}=\frac{-7-\sqrt{37}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{37}}{2*-1}=\frac{-7+\sqrt{37}}{-2}
$