3q^2-5q-8=9

Solution for 3q^2-5q-8=9 equation:

3q^2-5q-8=9

We move all terms to the left:

3q^2-5q-8-(9)=0

We add all the numbers together, and all the variables

3q^2-5q-17=0

a = 3; b = -5; c = -17;
Δ = b2-4ac
Δ = -52-4·3·(-17)
Δ = 229
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{-(-5)-\sqrt{229}}{2*3}=\frac{5-\sqrt{229}}{6}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{229}}{2*3}=\frac{5+\sqrt{229}}{6}
$