5q=31/q=13

Solution for 5q=31/q=13 equation:

5q=31/q=13

We move all terms to the left:

5q-(31/q)=0


Domain of the equation: q)!=0

q!=0/1

q!=0

q∈R


We add all the numbers together, and all the variables

5q-(+31/q)=0

We get rid of parentheses

5q-31/q=0

We multiply all the terms by the denominator


5q*q-31=0

Wy multiply elements

5q^2-31=0

a = 5; b = 0; c = -31;
Δ = b2-4ac
Δ = 02-4·5·(-31)
Δ = 620
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:

$\sqrt{\Delta}=\sqrt{620}=\sqrt{4*155}=\sqrt{4}*\sqrt{155}=2\sqrt{155}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{155}}{2*5}=\frac{0-2\sqrt{155}}{10}
=-\frac{2\sqrt{155}}{10}
=-\frac{\sqrt{155}}{5}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{155}}{2*5}=\frac{0+2\sqrt{155}}{10}
=\frac{2\sqrt{155}}{10}
=\frac{\sqrt{155}}{5}
$