3/5q=9-q

Solution for 3/5q=9-q equation:

3/5q=9-q

We move all terms to the left:

3/5q-(9-q)=0


Domain of the equation: 5q!=0

q!=0/5

q!=0

q∈R


We add all the numbers together, and all the variables

3/5q-(-1q+9)=0

We get rid of parentheses

3/5q+1q-9=0

We multiply all the terms by the denominator


1q*5q-9*5q+3=0

Wy multiply elements

5q^2-45q+3=0

a = 5; b = -45; c = +3;
Δ = b2-4ac
Δ = -452-4·5·3
Δ = 1965
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-\sqrt{1965}}{2*5}=\frac{45-\sqrt{1965}}{10}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{1965}}{2*5}=\frac{45+\sqrt{1965}}{10}
$