116y^2-348y+137=0

Solution for 116y^2-348y+137=0 equation:

116y^2-348y+137=0

a = 116; b = -348; c = +137;
Δ = b2-4ac
Δ = -3482-4·116·137
Δ = 57536
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:

$\sqrt{\Delta}=\sqrt{57536}=\sqrt{64*899}=\sqrt{64}*\sqrt{899}=8\sqrt{899}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-348)-8\sqrt{899}}{2*116}=\frac{348-8\sqrt{899}}{232}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-348)+8\sqrt{899}}{2*116}=\frac{348+8\sqrt{899}}{232}
$