(3y+11)4y=116

Solution for (3y+11)4y=116 equation:

(3y+11)4y=116

We move all terms to the left:

(3y+11)4y-(116)=0

We multiply parentheses

12y^2+44y-116=0

a = 12; b = 44; c = -116;
Δ = b2-4ac
Δ = 442-4·12·(-116)
Δ = 7504
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:

$\sqrt{\Delta}=\sqrt{7504}=\sqrt{16*469}=\sqrt{16}*\sqrt{469}=4\sqrt{469}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-4\sqrt{469}}{2*12}=\frac{-44-4\sqrt{469}}{24}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+4\sqrt{469}}{2*12}=\frac{-44+4\sqrt{469}}{24}
$