(12y+8)2y=50

Solution for (12y+8)2y=50 equation:

(12y+8)2y=50

We move all terms to the left:

(12y+8)2y-(50)=0

We multiply parentheses

24y^2+16y-50=0

a = 24; b = 16; c = -50;
Δ = b2-4ac
Δ = 162-4·24·(-50)
Δ = 5056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5056}=\sqrt{64*79}=\sqrt{64}*\sqrt{79}=8\sqrt{79}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-8\sqrt{79}}{2*24}=\frac{-16-8\sqrt{79}}{48}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+8\sqrt{79}}{2*24}=\frac{-16+8\sqrt{79}}{48}
$