4w^2+4w=1=75

Solution for 4w^2+4w=1=75 equation:

4w^2+4w=1=75

We move all terms to the left:

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

a = 4; b = 4; c = -1;
Δ = b2-4ac
Δ = 42-4·4·(-1)
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{2}}{2*4}=\frac{-4-4\sqrt{2}}{8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{2}}{2*4}=\frac{-4+4\sqrt{2}}{8}
$