8140=x^2-10x+65

Solution for 8140=x^2-10x+65 equation:

8140=x^2-10x+65

We move all terms to the left:

8140-(x^2-10x+65)=0

We get rid of parentheses

-x^2+10x-65+8140=0

We add all the numbers together, and all the variables

-1x^2+10x+8075=0

a = -1; b = 10; c = +8075;
Δ = b2-4ac
Δ = 102-4·(-1)·8075
Δ = 32400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32400}=180$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-180}{2*-1}=\frac{-190}{-2}
=+95
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+180}{2*-1}=\frac{170}{-2}
=-85
$