22=6(y-3)2y

Solution for 22=6(y-3)2y equation:

22=6(y-3)2y

We move all terms to the left:

22-(6(y-3)2y)=0


We calculate terms in parentheses: -(6(y-3)2y), so:

6(y-3)2y

We multiply parentheses

12y^2-36y

Back to the equation:

-(12y^2-36y)


We get rid of parentheses

-12y^2+36y+22=0

a = -12; b = 36; c = +22;
Δ = b2-4ac
Δ = 362-4·(-12)·22
Δ = 2352
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:

$\sqrt{\Delta}=\sqrt{2352}=\sqrt{784*3}=\sqrt{784}*\sqrt{3}=28\sqrt{3}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-28\sqrt{3}}{2*-12}=\frac{-36-28\sqrt{3}}{-24}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+28\sqrt{3}}{2*-12}=\frac{-36+28\sqrt{3}}{-24}
$