(7y+6)4y=166

Solution for (7y+6)4y=166 equation:

(7y+6)4y=166

We move all terms to the left:

(7y+6)4y-(166)=0

We multiply parentheses

28y^2+24y-166=0

a = 28; b = 24; c = -166;
Δ = b2-4ac
Δ = 242-4·28·(-166)
Δ = 19168
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:

$\sqrt{\Delta}=\sqrt{19168}=\sqrt{16*1198}=\sqrt{16}*\sqrt{1198}=4\sqrt{1198}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{1198}}{2*28}=\frac{-24-4\sqrt{1198}}{56}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{1198}}{2*28}=\frac{-24+4\sqrt{1198}}{56}
$