(8y+3)3y+6=97

Solution for (8y+3)3y+6=97 equation:

(8y+3)3y+6=97

We move all terms to the left:

(8y+3)3y+6-(97)=0

We add all the numbers together, and all the variables

(8y+3)3y-91=0

We multiply parentheses

24y^2+9y-91=0

a = 24; b = 9; c = -91;
Δ = b2-4ac
Δ = 92-4·24·(-91)
Δ = 8817
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{8817}}{2*24}=\frac{-9-\sqrt{8817}}{48}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{8817}}{2*24}=\frac{-9+\sqrt{8817}}{48}
$