8y(3y-21)=46

Solution for 8y(3y-21)=46 equation:

8y(3y-21)=46

We move all terms to the left:

8y(3y-21)-(46)=0

We multiply parentheses

24y^2-168y-46=0

a = 24; b = -168; c = -46;
Δ = b2-4ac
Δ = -1682-4·24·(-46)
Δ = 32640
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:

$\sqrt{\Delta}=\sqrt{32640}=\sqrt{64*510}=\sqrt{64}*\sqrt{510}=8\sqrt{510}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-168)-8\sqrt{510}}{2*24}=\frac{168-8\sqrt{510}}{48}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-168)+8\sqrt{510}}{2*24}=\frac{168+8\sqrt{510}}{48}
$