160q-2q^2=q

Solution for 160q-2q^2=q equation:

160q-2q^2=q

We move all terms to the left:

160q-2q^2-(q)=0

We add all the numbers together, and all the variables

-2q^2+159q=0

a = -2; b = 159; c = 0;
Δ = b2-4ac
Δ = 1592-4·(-2)·0
Δ = 25281
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25281}=159$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(159)-159}{2*-2}=\frac{-318}{-4}
=79+1/2
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(159)+159}{2*-2}=\frac{0}{-4}
=0
$