5q+2/3q=9-2q

Solution for 5q+2/3q=9-2q equation:

5q+2/3q=9-2q

We move all terms to the left:

5q+2/3q-(9-2q)=0


Domain of the equation: 3q!=0

q!=0/3

q!=0

q∈R


We add all the numbers together, and all the variables

5q+2/3q-(-2q+9)=0

We get rid of parentheses

5q+2/3q+2q-9=0

We multiply all the terms by the denominator


5q*3q+2q*3q-9*3q+2=0

Wy multiply elements

15q^2+6q^2-27q+2=0

We add all the numbers together, and all the variables

21q^2-27q+2=0

a = 21; b = -27; c = +2;
Δ = b2-4ac
Δ = -272-4·21·2
Δ = 561
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{-(-27)-\sqrt{561}}{2*21}=\frac{27-\sqrt{561}}{42}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{561}}{2*21}=\frac{27+\sqrt{561}}{42}
$