2(4y+7)6y=12

Solution for 2(4y+7)6y=12 equation:

2(4y+7)6y=12

We move all terms to the left:

2(4y+7)6y-(12)=0

We multiply parentheses

48y^2+84y-12=0

a = 48; b = 84; c = -12;
Δ = b2-4ac
Δ = 842-4·48·(-12)
Δ = 9360
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:

$\sqrt{\Delta}=\sqrt{9360}=\sqrt{144*65}=\sqrt{144}*\sqrt{65}=12\sqrt{65}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-12\sqrt{65}}{2*48}=\frac{-84-12\sqrt{65}}{96}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+12\sqrt{65}}{2*48}=\frac{-84+12\sqrt{65}}{96}
$