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

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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 $

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