-7y(y-8)=9y-24

Solution for -7y(y-8)=9y-24 equation:

-7y(y-8)=9y-24

We move all terms to the left:

-7y(y-8)-(9y-24)=0

We multiply parentheses

-7y^2+56y-(9y-24)=0

We get rid of parentheses

-7y^2+56y-9y+24=0

We add all the numbers together, and all the variables

-7y^2+47y+24=0

a = -7; b = 47; c = +24;
Δ = b2-4ac
Δ = 472-4·(-7)·24
Δ = 2881
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(47)-\sqrt{2881}}{2*-7}=\frac{-47-\sqrt{2881}}{-14}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(47)+\sqrt{2881}}{2*-7}=\frac{-47+\sqrt{2881}}{-14}
$