5y2+11y=-2

Solution for 5y2+11y=-2 equation:

5y^2+11y=-2

We move all terms to the left:

5y^2+11y-(-2)=0

We add all the numbers together, and all the variables

5y^2+11y+2=0

a = 5; b = 11; c = +2;
Δ = b2-4ac
Δ = 112-4·5·2
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-9}{2*5}=\frac{-20}{10}
=-2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+9}{2*5}=\frac{-2}{10}
=-1/5
$