(8y-9)(10y-3)=0

Solution for (8y-9)(10y-3)=0 equation:

(8y-9)(10y-3)=0

We multiply parentheses ..

(+80y^2-24y-90y+27)=0

We get rid of parentheses

80y^2-24y-90y+27=0

We add all the numbers together, and all the variables

80y^2-114y+27=0

a = 80; b = -114; c = +27;
Δ = b2-4ac
Δ = -1142-4·80·27
Δ = 4356
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4356}=66$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-114)-66}{2*80}=\frac{48}{160}
=3/10
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-114)+66}{2*80}=\frac{180}{160}
=1+1/8
$