52y^2-1y-27=0

Solution for 52y^2-1y-27=0 equation:

52y^2-1y-27=0

a = 52; b = -1; c = -27;
Δ = b2-4ac
Δ = -12-4·52·(-27)
Δ = 5617
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{5617}}{2*52}=\frac{1-\sqrt{5617}}{104}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{5617}}{2*52}=\frac{1+\sqrt{5617}}{104}
$