1/2x+1/5x=16

Solution for 1/2x+1/5x=16 equation:

1/2x+1/5x=16

We move all terms to the left:

1/2x+1/5x-(16)=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^2-16=0

We multiply all the terms by the denominator


5x+2x-16*10x^2=0

We add all the numbers together, and all the variables

7x-16*10x^2=0

Wy multiply elements

-160x^2+7x=0

a = -160; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-160)·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*-160}=\frac{-14}{-320}
=7/160
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-160}=\frac{0}{-320}
=0
$