11a^2+10a=-2

Solution for 11a^2+10a=-2 equation:

11a^2+10a=-2

We move all terms to the left:

11a^2+10a-(-2)=0

We add all the numbers together, and all the variables

11a^2+10a+2=0

a = 11; b = 10; c = +2;
Δ = b2-4ac
Δ = 102-4·11·2
Δ = 12
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{3}}{2*11}=\frac{-10-2\sqrt{3}}{22}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{3}}{2*11}=\frac{-10+2\sqrt{3}}{22}
$