1/5x-5=9-1/2x

Solution for 1/5x-5=9-1/2x equation:

1/5x-5=9-1/2x

We move all terms to the left:

1/5x-5-(9-1/2x)=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+9)-5=0

We get rid of parentheses

1/5x+1/2x-9-5=0

We calculate fractions


2x/10x^2+5x/10x^2-9-5=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

We add all the numbers together, and all the variables

7x-14*10x^2=0

Wy multiply elements

-140x^2+7x=0

a = -140; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-140)·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*-140}=\frac{-14}{-280}
=1/20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-140}=\frac{0}{-280}
=0
$