2y(y+8)=7(y+8)

Solution for 2y(y+8)=7(y+8) equation:

2y(y+8)=7(y+8)

We move all terms to the left:

2y(y+8)-(7(y+8))=0

We multiply parentheses

2y^2+16y-(7(y+8))=0


We calculate terms in parentheses: -(7(y+8)), so:

7(y+8)

We multiply parentheses

7y+56

Back to the equation:

-(7y+56)


We get rid of parentheses

2y^2+16y-7y-56=0

We add all the numbers together, and all the variables

2y^2+9y-56=0

a = 2; b = 9; c = -56;
Δ = b2-4ac
Δ = 92-4·2·(-56)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-23}{2*2}=\frac{-32}{4}
=-8
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+23}{2*2}=\frac{14}{4}
=3+1/2
$