11x^2+6x=-x^2+18

Solution for 11x^2+6x=-x^2+18 equation:

11x^2+6x=-x^2+18

We move all terms to the left:

11x^2+6x-(-x^2+18)=0

We get rid of parentheses

11x^2+x^2+6x-18=0

We add all the numbers together, and all the variables

12x^2+6x-18=0

a = 12; b = 6; c = -18;
Δ = b2-4ac
Δ = 62-4·12·(-18)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-30}{2*12}=\frac{-36}{24}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+30}{2*12}=\frac{24}{24}
=1
$