2(7-3y)3y=-4

Solution for 2(7-3y)3y=-4 equation:

2(7-3y)3y=-4

We move all terms to the left:

2(7-3y)3y-(-4)=0

We add all the numbers together, and all the variables

2(-3y+7)3y-(-4)=0

We add all the numbers together, and all the variables

2(-3y+7)3y+4=0

We multiply parentheses

-18y^2+42y+4=0

a = -18; b = 42; c = +4;
Δ = b2-4ac
Δ = 422-4·(-18)·4
Δ = 2052
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:

$\sqrt{\Delta}=\sqrt{2052}=\sqrt{36*57}=\sqrt{36}*\sqrt{57}=6\sqrt{57}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-6\sqrt{57}}{2*-18}=\frac{-42-6\sqrt{57}}{-36}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+6\sqrt{57}}{2*-18}=\frac{-42+6\sqrt{57}}{-36}
$