80y^2-120y+43=0

Solution for 80y^2-120y+43=0 equation:

80y^2-120y+43=0

a = 80; b = -120; c = +43;
Δ = b2-4ac
Δ = -1202-4·80·43
Δ = 640
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:

$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-8\sqrt{10}}{2*80}=\frac{120-8\sqrt{10}}{160}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+8\sqrt{10}}{2*80}=\frac{120+8\sqrt{10}}{160}
$