3q-2/4q=18

Solution for 3q-2/4q=18 equation:

3q-2/4q=18

We move all terms to the left:

3q-2/4q-(18)=0


Domain of the equation: 4q!=0

q!=0/4

q!=0

q∈R


We multiply all the terms by the denominator


3q*4q-18*4q-2=0

Wy multiply elements

12q^2-72q-2=0

a = 12; b = -72; c = -2;
Δ = b2-4ac
Δ = -722-4·12·(-2)
Δ = 5280
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5280}=\sqrt{16*330}=\sqrt{16}*\sqrt{330}=4\sqrt{330}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-4\sqrt{330}}{2*12}=\frac{72-4\sqrt{330}}{24}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+4\sqrt{330}}{2*12}=\frac{72+4\sqrt{330}}{24}
$