6(w+3)8w=4

Solution for 6(w+3)8w=4 equation:

6(w+3)8w=4

We move all terms to the left:

6(w+3)8w-(4)=0

We multiply parentheses

48w^2+144w-4=0

a = 48; b = 144; c = -4;
Δ = b2-4ac
Δ = 1442-4·48·(-4)
Δ = 21504
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:

$\sqrt{\Delta}=\sqrt{21504}=\sqrt{1024*21}=\sqrt{1024}*\sqrt{21}=32\sqrt{21}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-32\sqrt{21}}{2*48}=\frac{-144-32\sqrt{21}}{96}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+32\sqrt{21}}{2*48}=\frac{-144+32\sqrt{21}}{96}
$