17x-x^2=66

Solution for 17x-x^2=66 equation:

17x-x^2=66

We move all terms to the left:

17x-x^2-(66)=0

We add all the numbers together, and all the variables

-1x^2+17x-66=0

a = -1; b = 17; c = -66;
Δ = b2-4ac
Δ = 172-4·(-1)·(-66)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-5}{2*-1}=\frac{-22}{-2}
=+11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+5}{2*-1}=\frac{-12}{-2}
=+6
$