4y(y+8)=3(y+8)

Solution for 4y(y+8)=3(y+8) equation:

4y(y+8)=3(y+8)

We move all terms to the left:

4y(y+8)-(3(y+8))=0

We multiply parentheses

4y^2+32y-(3(y+8))=0


We calculate terms in parentheses: -(3(y+8)), so:

3(y+8)

We multiply parentheses

3y+24

Back to the equation:

-(3y+24)


We get rid of parentheses

4y^2+32y-3y-24=0

We add all the numbers together, and all the variables

4y^2+29y-24=0

a = 4; b = 29; c = -24;
Δ = b2-4ac
Δ = 292-4·4·(-24)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-35}{2*4}=\frac{-64}{8}
=-8
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+35}{2*4}=\frac{6}{8}
=3/4
$