(6-y)(5y-9)=0

Solution for (6-y)(5y-9)=0 equation:

(6-y)(5y-9)=0

We add all the numbers together, and all the variables

(-1y+6)(5y-9)=0

We multiply parentheses ..

(-5y^2+9y+30y-54)=0

We get rid of parentheses

-5y^2+9y+30y-54=0

We add all the numbers together, and all the variables

-5y^2+39y-54=0

a = -5; b = 39; c = -54;
Δ = b2-4ac
Δ = 392-4·(-5)·(-54)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-21}{2*-5}=\frac{-60}{-10}
=+6
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+21}{2*-5}=\frac{-18}{-10}
=1+4/5
$