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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-5y^2+30y-7y+42)=0

We get rid of parentheses

-5y^2+30y-7y+42=0

We add all the numbers together, and all the variables

-5y^2+23y+42=0

a = -5; b = 23; c = +42;
Δ = b2-4ac
Δ = 232-4·(-5)·42
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-37}{2*-5}=\frac{-60}{-10}
=+6
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+37}{2*-5}=\frac{14}{-10}
=-1+2/5
$