X^2+11x-9=2x^2+3x+6

Solution for X^2+11x-9=2x^2+3x+6 equation:

X^2+11X-9=2X^2+3X+6

We move all terms to the left:

X^2+11X-9-(2X^2+3X+6)=0

We get rid of parentheses

X^2-2X^2+11X-3X-6-9=0

We add all the numbers together, and all the variables

-1X^2+8X-15=0

a = -1; b = 8; c = -15;
Δ = b2-4ac
Δ = 82-4·(-1)·(-15)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2}{2*-1}=\frac{-10}{-2}
=+5
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2}{2*-1}=\frac{-6}{-2}
=+3
$