w2+28w+52=0

Solution for w2+28w+52=0 equation:

w2+28w+52=0

We add all the numbers together, and all the variables

w^2+28w+52=0

a = 1; b = 28; c = +52;
Δ = b2-4ac
Δ = 282-4·1·52
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-24}{2*1}=\frac{-52}{2}
=-26
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+24}{2*1}=\frac{-4}{2}
=-2
$