-1/2q+25=1/3q

Solution for -1/2q+25=1/3q equation:

-1/2q+25=1/3q

We move all terms to the left:

-1/2q+25-(1/3q)=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-(+1/3q)+25=0

We get rid of parentheses

-1/2q-1/3q+25=0

We calculate fractions


(-3q)/6q^2+(-2q)/6q^2+25=0

We multiply all the terms by the denominator


(-3q)+(-2q)+25*6q^2=0

Wy multiply elements

150q^2+(-3q)+(-2q)=0

We get rid of parentheses

150q^2-3q-2q=0

We add all the numbers together, and all the variables

150q^2-5q=0

a = 150; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·150·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*150}=\frac{0}{300}
=0
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*150}=\frac{10}{300}
=1/30
$