17x-x^2=70

Solution for 17x-x^2=70 equation:

17x-x^2=70

We move all terms to the left:

17x-x^2-(70)=0

We add all the numbers together, and all the variables

-1x^2+17x-70=0

a = -1; b = 17; c = -70;
Δ = b2-4ac
Δ = 172-4·(-1)·(-70)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-3}{2*-1}=\frac{-20}{-2}
=+10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+3}{2*-1}=\frac{-14}{-2}
=+7
$