5y(y+8)=4(y+8)

Solution for 5y(y+8)=4(y+8) equation:

5y(y+8)=4(y+8)

We move all terms to the left:

5y(y+8)-(4(y+8))=0

We multiply parentheses

5y^2+40y-(4(y+8))=0


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

4(y+8)

We multiply parentheses

4y+32

Back to the equation:

-(4y+32)


We get rid of parentheses

5y^2+40y-4y-32=0

We add all the numbers together, and all the variables

5y^2+36y-32=0

a = 5; b = 36; c = -32;
Δ = b2-4ac
Δ = 362-4·5·(-32)
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-44}{2*5}=\frac{-80}{10}
=-8
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+44}{2*5}=\frac{8}{10}
=4/5
$