1/2*q+3/5=2/3*q

Solution for 1/2*q+3/5=2/3*q equation:

1/2q+3/5=2/3q

We move all terms to the left:

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


Domain of the equation: 2q!=0

q!=0/2

q!=0

q∈R



Domain of the equation: 3q)!=0

q!=0/1

q!=0

q∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


54q^2/150q^2+75q/150q^2+(-100q)/150q^2=0

We multiply all the terms by the denominator


54q^2+75q+(-100q)=0

We get rid of parentheses

54q^2+75q-100q=0

We add all the numbers together, and all the variables

54q^2-25q=0

a = 54; b = -25; c = 0;
Δ = b2-4ac
Δ = -252-4·54·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-25}{2*54}=\frac{0}{108}
=0
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+25}{2*54}=\frac{50}{108}
=25/54
$