2(-6y+7)9y=14

Solution for 2(-6y+7)9y=14 equation:

2(-6y+7)9y=14

We move all terms to the left:

2(-6y+7)9y-(14)=0

We multiply parentheses

-108y^2+126y-14=0

a = -108; b = 126; c = -14;
Δ = b2-4ac
Δ = 1262-4·(-108)·(-14)
Δ = 9828
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:

$\sqrt{\Delta}=\sqrt{9828}=\sqrt{36*273}=\sqrt{36}*\sqrt{273}=6\sqrt{273}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(126)-6\sqrt{273}}{2*-108}=\frac{-126-6\sqrt{273}}{-216}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(126)+6\sqrt{273}}{2*-108}=\frac{-126+6\sqrt{273}}{-216}
$