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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

14y+2y(-1y+6)-6=0

We multiply parentheses

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

We add all the numbers together, and all the variables

-2y^2+26y-6=0

a = -2; b = 26; c = -6;
Δ = b2-4ac
Δ = 262-4·(-2)·(-6)
Δ = 628
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:

$\sqrt{\Delta}=\sqrt{628}=\sqrt{4*157}=\sqrt{4}*\sqrt{157}=2\sqrt{157}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{157}}{2*-2}=\frac{-26-2\sqrt{157}}{-4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{157}}{2*-2}=\frac{-26+2\sqrt{157}}{-4}
$