a^2-10a-85=0

Solution for a^2-10a-85=0 equation:

a^2-10a-85=0

a = 1; b = -10; c = -85;
Δ = b2-4ac
Δ = -102-4·1·(-85)
Δ = 440
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{440}=\sqrt{4*110}=\sqrt{4}*\sqrt{110}=2\sqrt{110}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{110}}{2*1}=\frac{10-2\sqrt{110}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{110}}{2*1}=\frac{10+2\sqrt{110}}{2}
$