6(y-4)5y=-46

Solution for 6(y-4)5y=-46 equation:

6(y-4)5y=-46

We move all terms to the left:

6(y-4)5y-(-46)=0

We add all the numbers together, and all the variables

6(y-4)5y+46=0

We multiply parentheses

30y^2-120y+46=0

a = 30; b = -120; c = +46;
Δ = b2-4ac
Δ = -1202-4·30·46
Δ = 8880
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:

$\sqrt{\Delta}=\sqrt{8880}=\sqrt{16*555}=\sqrt{16}*\sqrt{555}=4\sqrt{555}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-4\sqrt{555}}{2*30}=\frac{120-4\sqrt{555}}{60}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+4\sqrt{555}}{2*30}=\frac{120+4\sqrt{555}}{60}
$