(9y-4)(4y+5)=0

Solution for (9y-4)(4y+5)=0 equation:

(9y-4)(4y+5)=0

We multiply parentheses ..

(+36y^2+45y-16y-20)=0

We get rid of parentheses

36y^2+45y-16y-20=0

We add all the numbers together, and all the variables

36y^2+29y-20=0

a = 36; b = 29; c = -20;
Δ = b2-4ac
Δ = 292-4·36·(-20)
Δ = 3721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3721}=61$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-61}{2*36}=\frac{-90}{72}
=-1+1/4
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+61}{2*36}=\frac{32}{72}
=4/9
$