(5+w)2+w2=90

Solution for (5+w)2+w2=90 equation:

(5+w)2+w2=90

We move all terms to the left:

(5+w)2+w2-(90)=0

We add all the numbers together, and all the variables

(w+5)2+w2-90=0

We add all the numbers together, and all the variables

w^2+(w+5)2-90=0

We multiply parentheses

w^2+2w+10-90=0

We add all the numbers together, and all the variables

w^2+2w-80=0

a = 1; b = 2; c = -80;
Δ = b2-4ac
Δ = 22-4·1·(-80)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-18}{2*1}=\frac{-20}{2}
=-10
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+18}{2*1}=\frac{16}{2}
=8
$