(y-4)(5y+6)=0

Solution for (y-4)(5y+6)=0 equation:

(y-4)(5y+6)=0

We multiply parentheses ..

(+5y^2+6y-20y-24)=0

We get rid of parentheses

5y^2+6y-20y-24=0

We add all the numbers together, and all the variables

5y^2-14y-24=0

a = 5; b = -14; c = -24;
Δ = b2-4ac
Δ = -142-4·5·(-24)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-26}{2*5}=\frac{-12}{10}
=-1+1/5
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+26}{2*5}=\frac{40}{10}
=4
$