1/5x+1/10x=42

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
$