X^2-10x-85=2

Solution for X^2-10x-85=2 equation:

X^2-10X-85=2

We move all terms to the left:

X^2-10X-85-(2)=0

We add all the numbers together, and all the variables

X^2-10X-87=0

a = 1; b = -10; c = -87;
Δ = b2-4ac
Δ = -102-4·1·(-87)
Δ = 448
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:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-8\sqrt{7}}{2*1}=\frac{10-8\sqrt{7}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+8\sqrt{7}}{2*1}=\frac{10+8\sqrt{7}}{2}
$