2/5q+30=6-4/10q

Solution for 2/5q+30=6-4/10q equation:

2/5q+30=6-4/10q

We move all terms to the left:

2/5q+30-(6-4/10q)=0


Domain of the equation: 5q!=0

q!=0/5

q!=0

q∈R



Domain of the equation: 10q)!=0

q!=0/1

q!=0

q∈R


We add all the numbers together, and all the variables

2/5q-(-4/10q+6)+30=0

We get rid of parentheses

2/5q+4/10q-6+30=0

We calculate fractions


20q/50q^2+20q/50q^2-6+30=0

We add all the numbers together, and all the variables

20q/50q^2+20q/50q^2+24=0

We multiply all the terms by the denominator


20q+20q+24*50q^2=0

We add all the numbers together, and all the variables

40q+24*50q^2=0

Wy multiply elements

1200q^2+40q=0

a = 1200; b = 40; c = 0;
Δ = b2-4ac
Δ = 402-4·1200·0
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-40}{2*1200}=\frac{-80}{2400}
=-1/30
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+40}{2*1200}=\frac{0}{2400}
=0
$