17x-x^2=48

Solution for 17x-x^2=48 equation:

17x-x^2=48

We move all terms to the left:

17x-x^2-(48)=0

We add all the numbers together, and all the variables

-1x^2+17x-48=0

a = -1; b = 17; c = -48;
Δ = b2-4ac
Δ = 172-4·(-1)·(-48)
Δ = 97
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-\sqrt{97}}{2*-1}=\frac{-17-\sqrt{97}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{97}}{2*-1}=\frac{-17+\sqrt{97}}{-2}
$