-2/5q=1/10q-20

Solution for -2/5q=1/10q-20 equation:

-2/5q=1/10q-20

We move all terms to the left:

-2/5q-(1/10q-20)=0


Domain of the equation: 5q!=0

q!=0/5

q!=0

q∈R



Domain of the equation: 10q-20)!=0

q∈R


We get rid of parentheses

-2/5q-1/10q+20=0

We calculate fractions


(-20q)/50q^2+(-5q)/50q^2+20=0

We multiply all the terms by the denominator


(-20q)+(-5q)+20*50q^2=0

Wy multiply elements

1000q^2+(-20q)+(-5q)=0

We get rid of parentheses

1000q^2-20q-5q=0

We add all the numbers together, and all the variables

1000q^2-25q=0

a = 1000; b = -25; c = 0;
Δ = b2-4ac
Δ = -252-4·1000·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-25}{2*1000}=\frac{0}{2000}
=0
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+25}{2*1000}=\frac{50}{2000}
=1/40
$