w(2w+5)=52

Solution for w(2w+5)=52 equation:

w(2w+5)=52

We move all terms to the left:

w(2w+5)-(52)=0

We multiply parentheses

2w^2+5w-52=0

a = 2; b = 5; c = -52;
Δ = b2-4ac
Δ = 52-4·2·(-52)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-21}{2*2}=\frac{-26}{4}
=-6+1/2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+21}{2*2}=\frac{16}{4}
=4
$