85x2-766x+80=0

Solution for 85x2-766x+80=0 equation:

85x^2-766x+80=0

a = 85; b = -766; c = +80;
Δ = b2-4ac
Δ = -7662-4·85·80
Δ = 559556
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{559556}=\sqrt{4*139889}=\sqrt{4}*\sqrt{139889}=2\sqrt{139889}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-766)-2\sqrt{139889}}{2*85}=\frac{766-2\sqrt{139889}}{170}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-766)+2\sqrt{139889}}{2*85}=\frac{766+2\sqrt{139889}}{170}
$