w^2+2w+47=90

Solution for w^2+2w+47=90 equation:

w^2+2w+47=90

We move all terms to the left:

w^2+2w+47-(90)=0

We add all the numbers together, and all the variables

w^2+2w-43=0

a = 1; b = 2; c = -43;
Δ = b2-4ac
Δ = 22-4·1·(-43)
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-4\sqrt{11}}{2*1}=\frac{-2-4\sqrt{11}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+4\sqrt{11}}{2*1}=\frac{-2+4\sqrt{11}}{2}
$