4y-3y(y-6)+2=8

Solution for 4y-3y(y-6)+2=8 equation:

4y-3y(y-6)+2=8

We move all terms to the left:

4y-3y(y-6)+2-(8)=0

We add all the numbers together, and all the variables

4y-3y(y-6)-6=0

We multiply parentheses

-3y^2+4y+18y-6=0

We add all the numbers together, and all the variables

-3y^2+22y-6=0

a = -3; b = 22; c = -6;
Δ = b2-4ac
Δ = 222-4·(-3)·(-6)
Δ = 412
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:

$\sqrt{\Delta}=\sqrt{412}=\sqrt{4*103}=\sqrt{4}*\sqrt{103}=2\sqrt{103}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{103}}{2*-3}=\frac{-22-2\sqrt{103}}{-6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{103}}{2*-3}=\frac{-22+2\sqrt{103}}{-6}
$