8y(3-y-21)=46

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

8y(3-y-21)=46

We move all terms to the left:

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

We add all the numbers together, and all the variables

8y(-1y-18)-46=0

We multiply parentheses

-8y^2-144y-46=0

a = -8; b = -144; c = -46;
Δ = b2-4ac
Δ = -1442-4·(-8)·(-46)
Δ = 19264
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:

$\sqrt{\Delta}=\sqrt{19264}=\sqrt{64*301}=\sqrt{64}*\sqrt{301}=8\sqrt{301}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-8\sqrt{301}}{2*-8}=\frac{144-8\sqrt{301}}{-16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+8\sqrt{301}}{2*-8}=\frac{144+8\sqrt{301}}{-16}
$