3q*q-118.5q+328.5=0

Solution for 3q*q-118.5q+328.5=0 equation:

3q*q-118.5q+328.5=0

We add all the numbers together, and all the variables

-118.5q+3q*q+328.5=0

Wy multiply elements

3q^2-118.5q+328.5=0

a = 3; b = -118.5; c = +328.5;
Δ = b2-4ac
Δ = -118.52-4·3·328.5
Δ = 10100.25
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{-(-118.5)-\sqrt{10100.25}}{2*3}=\frac{118.5-\sqrt{10100.25}}{6}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-118.5)+\sqrt{10100.25}}{2*3}=\frac{118.5+\sqrt{10100.25}}{6}
$