7(y-8)+24=y(y-6)

Solution for 7(y-8)+24=y(y-6) equation:

7(y-8)+24=y(y-6)

We move all terms to the left:

7(y-8)+24-(y(y-6))=0

We multiply parentheses

7y-(y(y-6))-56+24=0


We calculate terms in parentheses: -(y(y-6)), so:

y(y-6)

We multiply parentheses

y^2-6y

Back to the equation:

-(y^2-6y)


We add all the numbers together, and all the variables

7y-(y^2-6y)-32=0

We get rid of parentheses

-y^2+7y+6y-32=0

We add all the numbers together, and all the variables

-1y^2+13y-32=0

a = -1; b = 13; c = -32;
Δ = b2-4ac
Δ = 132-4·(-1)·(-32)
Δ = 41
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{-(13)-\sqrt{41}}{2*-1}=\frac{-13-\sqrt{41}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{41}}{2*-1}=\frac{-13+\sqrt{41}}{-2}
$