w(13w+3)=10

Solution for w(13w+3)=10 equation:

w(13w+3)=10

We move all terms to the left:

w(13w+3)-(10)=0

We multiply parentheses

13w^2+3w-10=0

a = 13; b = 3; c = -10;
Δ = b2-4ac
Δ = 32-4·13·(-10)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-23}{2*13}=\frac{-26}{26}
=-1
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+23}{2*13}=\frac{20}{26}
=10/13
$