1/q=7/5q-11

Solution for 1/q=7/5q-11 equation:

1/q=7/5q-11

We move all terms to the left:

1/q-(7/5q-11)=0


Domain of the equation: q!=0

q∈R



Domain of the equation: 5q-11)!=0

q∈R


We get rid of parentheses

1/q-7/5q+11=0

We calculate fractions


5q/5q^2+(-7q)/5q^2+11=0

We multiply all the terms by the denominator


5q+(-7q)+11*5q^2=0

Wy multiply elements

55q^2+5q+(-7q)=0

We get rid of parentheses

55q^2+5q-7q=0

We add all the numbers together, and all the variables

55q^2-2q=0

a = 55; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·55·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*55}=\frac{0}{110}
=0
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*55}=\frac{4}{110}
=2/55
$