4w^2+4w+1=74

Solution for 4w^2+4w+1=74 equation:

4w^2+4w+1=74

We move all terms to the left:

4w^2+4w+1-(74)=0

We add all the numbers together, and all the variables

4w^2+4w-73=0

a = 4; b = 4; c = -73;
Δ = b2-4ac
Δ = 42-4·4·(-73)
Δ = 1184
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:

$\sqrt{\Delta}=\sqrt{1184}=\sqrt{16*74}=\sqrt{16}*\sqrt{74}=4\sqrt{74}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{74}}{2*4}=\frac{-4-4\sqrt{74}}{8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{74}}{2*4}=\frac{-4+4\sqrt{74}}{8}
$