(5y+22)(4y+27)=0

Solution for (5y+22)(4y+27)=0 equation:

(5y+22)(4y+27)=0

We multiply parentheses ..

(+20y^2+135y+88y+594)=0

We get rid of parentheses

20y^2+135y+88y+594=0

We add all the numbers together, and all the variables

20y^2+223y+594=0

a = 20; b = 223; c = +594;
Δ = b2-4ac
Δ = 2232-4·20·594
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(223)-47}{2*20}=\frac{-270}{40}
=-6+3/4
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(223)+47}{2*20}=\frac{-176}{40}
=-4+2/5
$