1/3q=9-2/5q

Solution for 1/3q=9-2/5q equation:

1/3q=9-2/5q

We move all terms to the left:

1/3q-(9-2/5q)=0


Domain of the equation: 3q!=0

q!=0/3

q!=0

q∈R



Domain of the equation: 5q)!=0

q!=0/1

q!=0

q∈R


We add all the numbers together, and all the variables

1/3q-(-2/5q+9)=0

We get rid of parentheses

1/3q+2/5q-9=0

We calculate fractions


5q/15q^2+6q/15q^2-9=0

We multiply all the terms by the denominator


5q+6q-9*15q^2=0

We add all the numbers together, and all the variables

11q-9*15q^2=0

Wy multiply elements

-135q^2+11q=0

a = -135; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-135)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-135}=\frac{-22}{-270}
=11/135
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-135}=\frac{0}{-270}
=0
$