x^2-37x+85=0

Solution for x^2-37x+85=0 equation:

x^2-37x+85=0

a = 1; b = -37; c = +85;
Δ = b2-4ac
Δ = -372-4·1·85
Δ = 1029
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:

$\sqrt{\Delta}=\sqrt{1029}=\sqrt{49*21}=\sqrt{49}*\sqrt{21}=7\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37)-7\sqrt{21}}{2*1}=\frac{37-7\sqrt{21}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+7\sqrt{21}}{2*1}=\frac{37+7\sqrt{21}}{2}
$