41y^2-4y=172

Solution for 41y^2-4y=172 equation:

41y^2-4y=172

We move all terms to the left:

41y^2-4y-(172)=0

a = 41; b = -4; c = -172;
Δ = b2-4ac
Δ = -42-4·41·(-172)
Δ = 28224
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{28224}=168$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-168}{2*41}=\frac{-164}{82}
=-2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+168}{2*41}=\frac{172}{82}
=2+4/41
$