116y^2-348y+177=0

Solution for 116y^2-348y+177=0 equation:

116y^2-348y+177=0

a = 116; b = -348; c = +177;
Δ = b2-4ac
Δ = -3482-4·116·177
Δ = 38976
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:

$\sqrt{\Delta}=\sqrt{38976}=\sqrt{64*609}=\sqrt{64}*\sqrt{609}=8\sqrt{609}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-348)-8\sqrt{609}}{2*116}=\frac{348-8\sqrt{609}}{232}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-348)+8\sqrt{609}}{2*116}=\frac{348+8\sqrt{609}}{232}
$