(2y-7)(3-y)=0

Solution for (2y-7)(3-y)=0 equation:

(2y-7)(3-y)=0

We add all the numbers together, and all the variables

(2y-7)(-1y+3)=0

We multiply parentheses ..

(-2y^2+6y+7y-21)=0

We get rid of parentheses

-2y^2+6y+7y-21=0

We add all the numbers together, and all the variables

-2y^2+13y-21=0

a = -2; b = 13; c = -21;
Δ = b2-4ac
Δ = 132-4·(-2)·(-21)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-1}{2*-2}=\frac{-14}{-4}
=3+1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+1}{2*-2}=\frac{-12}{-4}
=+3
$