15/5q=q

Solution for 15/5q=q equation:

15/5q=q

We move all terms to the left:

15/5q-(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

-1q+15/5q=0

We multiply all the terms by the denominator


-1q*5q+15=0

Wy multiply elements

-5q^2+15=0

a = -5; b = 0; c = +15;
Δ = b2-4ac
Δ = 02-4·(-5)·15
Δ = 300
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:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{3}}{2*-5}=\frac{0-10\sqrt{3}}{-10}
=-\frac{10\sqrt{3}}{-10}
=-\frac{\sqrt{3}}{-1}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{3}}{2*-5}=\frac{0+10\sqrt{3}}{-10}
=\frac{10\sqrt{3}}{-10}
=\frac{\sqrt{3}}{-1}
$