2y(y+8)=(5y+8)

Solution for 2y(y+8)=(5y+8) equation:

2y(y+8)=(5y+8)

We move all terms to the left:

2y(y+8)-((5y+8))=0

We multiply parentheses

2y^2+16y-((5y+8))=0


We calculate terms in parentheses: -((5y+8)), so:

(5y+8)

We get rid of parentheses

5y+8

Back to the equation:

-(5y+8)


We get rid of parentheses

2y^2+16y-5y-8=0

We add all the numbers together, and all the variables

2y^2+11y-8=0

a = 2; b = 11; c = -8;
Δ = b2-4ac
Δ = 112-4·2·(-8)
Δ = 185
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{-(11)-\sqrt{185}}{2*2}=\frac{-11-\sqrt{185}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{185}}{2*2}=\frac{-11+\sqrt{185}}{4}
$