1/5x+30=1/2x-5

Solution for 1/5x+30=1/2x-5 equation:

1/5x+30=1/2x-5

We move all terms to the left:

1/5x+30-(1/2x-5)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 2x-5)!=0

x∈R


We get rid of parentheses

1/5x-1/2x+5+30=0

We calculate fractions


2x/10x^2+(-5x)/10x^2+5+30=0

We add all the numbers together, and all the variables

2x/10x^2+(-5x)/10x^2+35=0

We multiply all the terms by the denominator


2x+(-5x)+35*10x^2=0

Wy multiply elements

350x^2+2x+(-5x)=0

We get rid of parentheses

350x^2+2x-5x=0

We add all the numbers together, and all the variables

350x^2-3x=0

a = 350; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·350·0
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*350}=\frac{0}{700}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*350}=\frac{6}{700}
=3/350
$