3,5q=1/2q

Solution for 3,5q=1/2q equation:

3.5q=1/2q

We move all terms to the left:

3.5q-(1/2q)=0


Domain of the equation: 2q)!=0

q!=0/1

q!=0

q∈R


We add all the numbers together, and all the variables

3.5q-(+1/2q)=0

We get rid of parentheses

3.5q-1/2q=0

We multiply all the terms by the denominator


(3.5q)*2q-1=0

We add all the numbers together, and all the variables

(+3.5q)*2q-1=0

We multiply parentheses

6q^2-1=0

a = 6; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·6·(-1)
Δ = 24
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{6}}{2*6}=\frac{0-2\sqrt{6}}{12}
=-\frac{2\sqrt{6}}{12}
=-\frac{\sqrt{6}}{6}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{6}}{2*6}=\frac{0+2\sqrt{6}}{12}
=\frac{2\sqrt{6}}{12}
=\frac{\sqrt{6}}{6}
$