2w+w^2=60

Solution for 2w+w^2=60 equation:

2w+w^2=60

We move all terms to the left:

2w+w^2-(60)=0

a = 1; b = 2; c = -60;
Δ = b2-4ac
Δ = 22-4·1·(-60)
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{61}}{2*1}=\frac{-2-2\sqrt{61}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{61}}{2*1}=\frac{-2+2\sqrt{61}}{2}
$