8(w-3)6w=-32

Solution for 8(w-3)6w=-32 equation:

8(w-3)6w=-32

We move all terms to the left:

8(w-3)6w-(-32)=0

We add all the numbers together, and all the variables

8(w-3)6w+32=0

We multiply parentheses

48w^2-144w+32=0

a = 48; b = -144; c = +32;
Δ = b2-4ac
Δ = -1442-4·48·32
Δ = 14592
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:

$\sqrt{\Delta}=\sqrt{14592}=\sqrt{256*57}=\sqrt{256}*\sqrt{57}=16\sqrt{57}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-16\sqrt{57}}{2*48}=\frac{144-16\sqrt{57}}{96}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+16\sqrt{57}}{2*48}=\frac{144+16\sqrt{57}}{96}
$