(24y^2)-3y=6

Solution for (24y^2)-3y=6 equation:

(24y^2)-3y=6

We move all terms to the left:

(24y^2)-3y-(6)=0

a = 24; b = -3; c = -6;
Δ = b2-4ac
Δ = -32-4·24·(-6)
Δ = 585
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{585}=\sqrt{9*65}=\sqrt{9}*\sqrt{65}=3\sqrt{65}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{65}}{2*24}=\frac{3-3\sqrt{65}}{48}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{65}}{2*24}=\frac{3+3\sqrt{65}}{48}
$