17q-q^2=72

Solution for 17q-q^2=72 equation:

17q-q^2=72

We move all terms to the left:

17q-q^2-(72)=0

We add all the numbers together, and all the variables

-1q^2+17q-72=0

a = -1; b = 17; c = -72;
Δ = b2-4ac
Δ = 172-4·(-1)·(-72)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-1}{2*-1}=\frac{-18}{-2}
=+9
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+1}{2*-1}=\frac{-16}{-2}
=+8
$