q2+12.53=16.53q

Solution for q2+12.53=16.53q equation:

q2+12.53=16.53q

We move all terms to the left:

q2+12.53-(16.53q)=0

We add all the numbers together, and all the variables

q2-(+16.53q)+12.53=0

We add all the numbers together, and all the variables

q^2-(+16.53q)+12.53=0

We get rid of parentheses

q^2-16.53q+12.53=0

a = 1; b = -16.53; c = +12.53;
Δ = b2-4ac
Δ = -16.532-4·1·12.53
Δ = 223.1209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16.53)-\sqrt{223.1209}}{2*1}=\frac{16.53-\sqrt{223.1209}}{2}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16.53)+\sqrt{223.1209}}{2*1}=\frac{16.53+\sqrt{223.1209}}{2}
$