89x^2-218x+85=0

Solution for 89x^2-218x+85=0 equation:

89x^2-218x+85=0

a = 89; b = -218; c = +85;
Δ = b2-4ac
Δ = -2182-4·89·85
Δ = 17264
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:

$\sqrt{\Delta}=\sqrt{17264}=\sqrt{16*1079}=\sqrt{16}*\sqrt{1079}=4\sqrt{1079}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-218)-4\sqrt{1079}}{2*89}=\frac{218-4\sqrt{1079}}{178}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-218)+4\sqrt{1079}}{2*89}=\frac{218+4\sqrt{1079}}{178}
$