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

Solution for (8-y)(4y-9)=0 equation:

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

We add all the numbers together, and all the variables

(-1y+8)(4y-9)=0

We multiply parentheses ..

(-4y^2+9y+32y-72)=0

We get rid of parentheses

-4y^2+9y+32y-72=0

We add all the numbers together, and all the variables

-4y^2+41y-72=0

a = -4; b = 41; c = -72;
Δ = b2-4ac
Δ = 412-4·(-4)·(-72)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(41)-23}{2*-4}=\frac{-64}{-8}
=+8
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+23}{2*-4}=\frac{-18}{-8}
=2+1/4
$