x^2-85x-400=0

Solution for x^2-85x-400=0 equation:

x^2-85x-400=0

a = 1; b = -85; c = -400;
Δ = b2-4ac
Δ = -852-4·1·(-400)
Δ = 8825
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:

$\sqrt{\Delta}=\sqrt{8825}=\sqrt{25*353}=\sqrt{25}*\sqrt{353}=5\sqrt{353}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-85)-5\sqrt{353}}{2*1}=\frac{85-5\sqrt{353}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-85)+5\sqrt{353}}{2*1}=\frac{85+5\sqrt{353}}{2}
$