2w(w+5)=40

Solution for 2w(w+5)=40 equation:

2w(w+5)=40

We move all terms to the left:

2w(w+5)-(40)=0

We multiply parentheses

2w^2+10w-40=0

a = 2; b = 10; c = -40;
Δ = b2-4ac
Δ = 102-4·2·(-40)
Δ = 420
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:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{105}}{2*2}=\frac{-10-2\sqrt{105}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{105}}{2*2}=\frac{-10+2\sqrt{105}}{4}
$