x^2=10x+85

Solution for x^2=10x+85 equation:

x^2=10x+85

We move all terms to the left:

x^2-(10x+85)=0

We get rid of parentheses

x^2-10x-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:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

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