1/2x+1/5x=2

Solution for 1/2x+1/5x=2 equation:

1/2x+1/5x=2

We move all terms to the left:

1/2x+1/5x-(2)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We calculate fractions


5x/10x^2+2x/10x^2-2=0

We multiply all the terms by the denominator


5x+2x-2*10x^2=0

We add all the numbers together, and all the variables

7x-2*10x^2=0

Wy multiply elements

-20x^2+7x=0

a = -20; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-20)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-20}=\frac{-14}{-40}
=7/20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-20}=\frac{0}{-40}
=0
$