(5y-6)(7-y)=0

Solution for (5y-6)(7-y)=0 equation:

(5y-6)(7-y)=0

We add all the numbers together, and all the variables

(5y-6)(-1y+7)=0

We multiply parentheses ..

(-5y^2+35y+6y-42)=0

We get rid of parentheses

-5y^2+35y+6y-42=0

We add all the numbers together, and all the variables

-5y^2+41y-42=0

a = -5; b = 41; c = -42;
Δ = b2-4ac
Δ = 412-4·(-5)·(-42)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(41)-29}{2*-5}=\frac{-70}{-10}
=+7
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+29}{2*-5}=\frac{-12}{-10}
=1+1/5
$