9=4y(y-2)

Solution for 9=4y(y-2) equation:

9=4y(y-2)

We move all terms to the left:

9-(4y(y-2))=0


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

4y(y-2)

We multiply parentheses

4y^2-8y

Back to the equation:

-(4y^2-8y)


We get rid of parentheses

-4y^2+8y+9=0

a = -4; b = 8; c = +9;
Δ = b2-4ac
Δ = 82-4·(-4)·9
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{13}}{2*-4}=\frac{-8-4\sqrt{13}}{-8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{13}}{2*-4}=\frac{-8+4\sqrt{13}}{-8}
$