1/5x+5=19+1/2x

Solution for 1/5x+5=19+1/2x equation:

1/5x+5=19+1/2x

We move all terms to the left:

1/5x+5-(19+1/2x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/5x-(1/2x+19)+5=0

We get rid of parentheses

1/5x-1/2x-19+5=0

We calculate fractions


2x/10x^2+(-5x)/10x^2-19+5=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


2x+(-5x)-14*10x^2=0

Wy multiply elements

-140x^2+2x+(-5x)=0

We get rid of parentheses

-140x^2+2x-5x=0

We add all the numbers together, and all the variables

-140x^2-3x=0

a = -140; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-140)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-140}=\frac{0}{-280}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-140}=\frac{6}{-280}
=-3/140
$