2(5y-2)-22=11y(-3y+6)

Solution for 2(5y-2)-22=11y(-3y+6) equation:

2(5y-2)-22=11y(-3y+6)

We move all terms to the left:

2(5y-2)-22-(11y(-3y+6))=0

We multiply parentheses

10y-(11y(-3y+6))-4-22=0


We calculate terms in parentheses: -(11y(-3y+6)), so:

11y(-3y+6)

We multiply parentheses

-33y^2+66y

Back to the equation:

-(-33y^2+66y)


We add all the numbers together, and all the variables

-(-33y^2+66y)+10y-26=0

We get rid of parentheses

33y^2-66y+10y-26=0

We add all the numbers together, and all the variables

33y^2-56y-26=0

a = 33; b = -56; c = -26;
Δ = b2-4ac
Δ = -562-4·33·(-26)
Δ = 6568
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:

$\sqrt{\Delta}=\sqrt{6568}=\sqrt{4*1642}=\sqrt{4}*\sqrt{1642}=2\sqrt{1642}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-2\sqrt{1642}}{2*33}=\frac{56-2\sqrt{1642}}{66}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+2\sqrt{1642}}{2*33}=\frac{56+2\sqrt{1642}}{66}
$