1/2x-5=1/5x+7

Solution for 1/2x-5=1/5x+7 equation:

1/2x-5=1/5x+7

We move all terms to the left:

1/2x-5-(1/5x+7)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 5x+7)!=0

x∈R


We get rid of parentheses

1/2x-1/5x-7-5=0

We calculate fractions


5x/10x^2+(-2x)/10x^2-7-5=0

We add all the numbers together, and all the variables

5x/10x^2+(-2x)/10x^2-12=0

We multiply all the terms by the denominator


5x+(-2x)-12*10x^2=0

Wy multiply elements

-120x^2+5x+(-2x)=0

We get rid of parentheses

-120x^2+5x-2x=0

We add all the numbers together, and all the variables

-120x^2+3x=0

a = -120; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-120)·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*-120}=\frac{-6}{-240}
=1/40
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-120}=\frac{0}{-240}
=0
$