(3y-7)(8+y)=0

Solution for (3y-7)(8+y)=0 equation:

(3y-7)(8+y)=0

We add all the numbers together, and all the variables

(3y-7)(y+8)=0

We multiply parentheses ..

(+3y^2+24y-7y-56)=0

We get rid of parentheses

3y^2+24y-7y-56=0

We add all the numbers together, and all the variables

3y^2+17y-56=0

a = 3; b = 17; c = -56;
Δ = b2-4ac
Δ = 172-4·3·(-56)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-31}{2*3}=\frac{-48}{6}
=-8
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+31}{2*3}=\frac{14}{6}
=2+1/3
$