2x^2+11x+5=-5

Solution for 2x^2+11x+5=-5 equation:

2x^2+11x+5=-5

We move all terms to the left:

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

We add all the numbers together, and all the variables

2x^2+11x+10=0

a = 2; b = 11; c = +10;
Δ = b2-4ac
Δ = 112-4·2·10
Δ = 41
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-\sqrt{41}}{2*2}=\frac{-11-\sqrt{41}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{41}}{2*2}=\frac{-11+\sqrt{41}}{4}
$