1/2q=2/q-5

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

1/2q=2/q-5

We move all terms to the left:

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


Domain of the equation: 2q!=0

q!=0/2

q!=0

q∈R



Domain of the equation: q-5)!=0

q∈R


We get rid of parentheses

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

We calculate fractions


q/2q^2+(-4q)/2q^2+5=0

We multiply all the terms by the denominator


q+(-4q)+5*2q^2=0

Wy multiply elements

10q^2+q+(-4q)=0

We get rid of parentheses

10q^2+q-4q=0

We add all the numbers together, and all the variables

10q^2-3q=0

a = 10; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·10·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*10}=\frac{0}{20}
=0
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*10}=\frac{6}{20}
=3/10
$