(5y+9)(y-10)=0

Solution for (5y+9)(y-10)=0 equation:

(5y+9)(y-10)=0

We multiply parentheses ..

(+5y^2-50y+9y-90)=0

We get rid of parentheses

5y^2-50y+9y-90=0

We add all the numbers together, and all the variables

5y^2-41y-90=0

a = 5; b = -41; c = -90;
Δ = b2-4ac
Δ = -412-4·5·(-90)
Δ = 3481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3481}=59$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-41)-59}{2*5}=\frac{-18}{10}
=-1+4/5
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-41)+59}{2*5}=\frac{100}{10}
=10
$