2/3q-9=2/5q

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

2/3q-9=2/5q

We move all terms to the left:

2/3q-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

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

We get rid of parentheses

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

We calculate fractions


10q/15q^2+(-6q)/15q^2-9=0

We multiply all the terms by the denominator


10q+(-6q)-9*15q^2=0

Wy multiply elements

-135q^2+10q+(-6q)=0

We get rid of parentheses

-135q^2+10q-6q=0

We add all the numbers together, and all the variables

-135q^2+4q=0

a = -135; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-135)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-135}=\frac{-8}{-270}
=4/135
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-135}=\frac{0}{-270}
=0
$