3(y-2)2y=4y+14

Solution for 3(y-2)2y=4y+14 equation:

3(y-2)2y=4y+14

We move all terms to the left:

3(y-2)2y-(4y+14)=0

We multiply parentheses

6y^2-12y-(4y+14)=0

We get rid of parentheses

6y^2-12y-4y-14=0

We add all the numbers together, and all the variables

6y^2-16y-14=0

a = 6; b = -16; c = -14;
Δ = b2-4ac
Δ = -162-4·6·(-14)
Δ = 592
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:

$\sqrt{\Delta}=\sqrt{592}=\sqrt{16*37}=\sqrt{16}*\sqrt{37}=4\sqrt{37}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{37}}{2*6}=\frac{16-4\sqrt{37}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{37}}{2*6}=\frac{16+4\sqrt{37}}{12}
$