4y(7y+6)=116

Solution for 4y(7y+6)=116 equation:

4y(7y+6)=116

We move all terms to the left:

4y(7y+6)-(116)=0

We multiply parentheses

28y^2+24y-116=0

a = 28; b = 24; c = -116;
Δ = b2-4ac
Δ = 242-4·28·(-116)
Δ = 13568
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:

$\sqrt{\Delta}=\sqrt{13568}=\sqrt{256*53}=\sqrt{256}*\sqrt{53}=16\sqrt{53}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-16\sqrt{53}}{2*28}=\frac{-24-16\sqrt{53}}{56}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+16\sqrt{53}}{2*28}=\frac{-24+16\sqrt{53}}{56}
$