1/5q=q-2/5q

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

1/5q=q-2/5q

We move all terms to the left:

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


Domain of the equation: 5q!=0

q!=0/5

q!=0

q∈R



Domain of the equation: 5q)!=0

q!=0/1

q!=0

q∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


-q*5q+1+2=0

We add all the numbers together, and all the variables

-q*5q+3=0

Wy multiply elements

-5q^2+3=0

a = -5; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-5)·3
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{15}}{2*-5}=\frac{0-2\sqrt{15}}{-10}
=-\frac{2\sqrt{15}}{-10}
=-\frac{\sqrt{15}}{-5}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{15}}{2*-5}=\frac{0+2\sqrt{15}}{-10}
=\frac{2\sqrt{15}}{-10}
=\frac{\sqrt{15}}{-5}
$