4w^2+4w=121

Solution for 4w^2+4w=121 equation:

4w^2+4w=121

We move all terms to the left:

4w^2+4w-(121)=0

a = 4; b = 4; c = -121;
Δ = b2-4ac
Δ = 42-4·4·(-121)
Δ = 1952
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1952}=\sqrt{16*122}=\sqrt{16}*\sqrt{122}=4\sqrt{122}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{122}}{2*4}=\frac{-4-4\sqrt{122}}{8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{122}}{2*4}=\frac{-4+4\sqrt{122}}{8}
$