22=4y(5y-2)

Solution for 22=4y(5y-2) equation:

22=4y(5y-2)

We move all terms to the left:

22-(4y(5y-2))=0


We calculate terms in parentheses: -(4y(5y-2)), so:

4y(5y-2)

We multiply parentheses

20y^2-8y

Back to the equation:

-(20y^2-8y)


We get rid of parentheses

-20y^2+8y+22=0

a = -20; b = 8; c = +22;
Δ = b2-4ac
Δ = 82-4·(-20)·22
Δ = 1824
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:

$\sqrt{\Delta}=\sqrt{1824}=\sqrt{16*114}=\sqrt{16}*\sqrt{114}=4\sqrt{114}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{114}}{2*-20}=\frac{-8-4\sqrt{114}}{-40}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{114}}{2*-20}=\frac{-8+4\sqrt{114}}{-40}
$