6x-x^2=-17

Solution for 6x-x^2=-17 equation:

6x-x^2=-17

We move all terms to the left:

6x-x^2-(-17)=0

We add all the numbers together, and all the variables

-1x^2+6x+17=0

a = -1; b = 6; c = +17;
Δ = b2-4ac
Δ = 62-4·(-1)·17
Δ = 104
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:

$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{26}}{2*-1}=\frac{-6-2\sqrt{26}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{26}}{2*-1}=\frac{-6+2\sqrt{26}}{-2}
$