2a^2+6a=-9a^2+9a+11

Solution for 2a^2+6a=-9a^2+9a+11 equation:

2a^2+6a=-9a^2+9a+11

We move all terms to the left:

2a^2+6a-(-9a^2+9a+11)=0

We get rid of parentheses

2a^2+9a^2-9a+6a-11=0

We add all the numbers together, and all the variables

11a^2-3a-11=0

a = 11; b = -3; c = -11;
Δ = b2-4ac
Δ = -32-4·11·(-11)
Δ = 493
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{493}}{2*11}=\frac{3-\sqrt{493}}{22}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{493}}{2*11}=\frac{3+\sqrt{493}}{22}
$