8w^2-((5w^2)+13w-6)=0

Solution for 8w^2-((5w^2)+13w-6)=0 equation:

8w^2-((5w^2)+13w-6)=0

We get rid of parentheses

8w^2-5w^2-13w+6=0

We add all the numbers together, and all the variables

3w^2-13w+6=0

a = 3; b = -13; c = +6;
Δ = b2-4ac
Δ = -132-4·3·6
Δ = 97
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-\sqrt{97}}{2*3}=\frac{13-\sqrt{97}}{6}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{97}}{2*3}=\frac{13+\sqrt{97}}{6}
$