4w^2+11w+3=-1

Solution for 4w^2+11w+3=-1 equation:

4w^2+11w+3=-1

We move all terms to the left:

4w^2+11w+3-(-1)=0

We add all the numbers together, and all the variables

4w^2+11w+4=0

a = 4; b = 11; c = +4;
Δ = b2-4ac
Δ = 112-4·4·4
Δ = 57
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-\sqrt{57}}{2*4}=\frac{-11-\sqrt{57}}{8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{57}}{2*4}=\frac{-11+\sqrt{57}}{8}
$