10x-x^2=17

Solution for 10x-x^2=17 equation:

10x-x^2=17

We move all terms to the left:

10x-x^2-(17)=0

We add all the numbers together, and all the variables

-1x^2+10x-17=0

a = -1; b = 10; c = -17;
Δ = b2-4ac
Δ = 102-4·(-1)·(-17)
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-4\sqrt{2}}{2*-1}=\frac{-10-4\sqrt{2}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+4\sqrt{2}}{2*-1}=\frac{-10+4\sqrt{2}}{-2}
$