1/5x+1/10x=42

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Solution for 1/5x+1/10x=42 equation:



1/5x+1/10x=42
We move all terms to the left:
1/5x+1/10x-(42)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
Domain of the equation: 10x!=0
x!=0/10
x!=0
x∈R
We calculate fractions
10x/50x^2+5x/50x^2-42=0
We multiply all the terms by the denominator
10x+5x-42*50x^2=0
We add all the numbers together, and all the variables
15x-42*50x^2=0
Wy multiply elements
-2100x^2+15x=0
a = -2100; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·(-2100)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*-2100}=\frac{-30}{-4200} =1/140 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*-2100}=\frac{0}{-4200} =0 $

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