w(13w+5)=8

Solution for w(13w+5)=8 equation:

w(13w+5)=8

We move all terms to the left:

w(13w+5)-(8)=0

We multiply parentheses

13w^2+5w-8=0

a = 13; b = 5; c = -8;
Δ = b2-4ac
Δ = 52-4·13·(-8)
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*13}=\frac{-26}{26}
=-1
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+21}{2*13}=\frac{16}{26}
=8/13
$