10x-x2=1

Solution for 10x-x2=1 equation:

10x-x2=1

We move all terms to the left:

10x-x2-(1)=0

We add all the numbers together, and all the variables

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

a = -1; b = 10; c = -1;
Δ = b2-4ac
Δ = 102-4·(-1)·(-1)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-4\sqrt{6}}{2*-1}=\frac{-10-4\sqrt{6}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+4\sqrt{6}}{2*-1}=\frac{-10+4\sqrt{6}}{-2}
$