5(y+6)+4=9(y+4)(y-2)

Solution for 5(y+6)+4=9(y+4)(y-2) equation:

5(y+6)+4=9(y+4)(y-2)

We move all terms to the left:

5(y+6)+4-(9(y+4)(y-2))=0

We multiply parentheses

5y-(9(y+4)(y-2))+30+4=0

We multiply parentheses ..

-(9(+y^2-2y+4y-8))+5y+30+4=0


We calculate terms in parentheses: -(9(+y^2-2y+4y-8)), so:

9(+y^2-2y+4y-8)

We multiply parentheses

9y^2-18y+36y-72

We add all the numbers together, and all the variables

9y^2+18y-72

Back to the equation:

-(9y^2+18y-72)


We add all the numbers together, and all the variables

5y-(9y^2+18y-72)+34=0

We get rid of parentheses

-9y^2+5y-18y+72+34=0

We add all the numbers together, and all the variables

-9y^2-13y+106=0

a = -9; b = -13; c = +106;
Δ = b2-4ac
Δ = -132-4·(-9)·106
Δ = 3985
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{3985}}{2*-9}=\frac{13-\sqrt{3985}}{-18}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{3985}}{2*-9}=\frac{13+\sqrt{3985}}{-18}
$