8(y2-1)=3(16+3y)

Solution for 8(y2-1)=3(16+3y) equation:

8(y2-1)=3(16+3y)

We move all terms to the left:

8(y2-1)-(3(16+3y))=0

We add all the numbers together, and all the variables

8(+y^2-1)-(3(3y+16))=0

We multiply parentheses

8y^2-(3(3y+16))-8=0


We calculate terms in parentheses: -(3(3y+16)), so:

3(3y+16)

We multiply parentheses

9y+48

Back to the equation:

-(9y+48)


We get rid of parentheses

8y^2-9y-48-8=0

We add all the numbers together, and all the variables

8y^2-9y-56=0

a = 8; b = -9; c = -56;
Δ = b2-4ac
Δ = -92-4·8·(-56)
Δ = 1873
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{-(-9)-\sqrt{1873}}{2*8}=\frac{9-\sqrt{1873}}{16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{1873}}{2*8}=\frac{9+\sqrt{1873}}{16}
$