2/5x+16=14-3/10x

Solution for 2/5x+16=14-3/10x equation:

2/5x+16=14-3/10x

We move all terms to the left:

2/5x+16-(14-3/10x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2/5x-(-3/10x+14)+16=0

We get rid of parentheses

2/5x+3/10x-14+16=0

We calculate fractions


20x/50x^2+15x/50x^2-14+16=0

We add all the numbers together, and all the variables

20x/50x^2+15x/50x^2+2=0

We multiply all the terms by the denominator


20x+15x+2*50x^2=0

We add all the numbers together, and all the variables

35x+2*50x^2=0

Wy multiply elements

100x^2+35x=0

a = 100; b = 35; c = 0;
Δ = b2-4ac
Δ = 352-4·100·0
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-35}{2*100}=\frac{-70}{200}
=-7/20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+35}{2*100}=\frac{0}{200}
=0
$