1/2x-3/5=-1/5x+5

Solution for 1/2x-3/5=-1/5x+5 equation:

1/2x-3/5=-1/5x+5

We move all terms to the left:

1/2x-3/5-(-1/5x+5)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



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

x∈R


We get rid of parentheses

1/2x+1/5x-5-3/5=0

We calculate fractions


125x/250x^2+2x/250x^2+(-6x)/250x^2-5=0

We multiply all the terms by the denominator


125x+2x+(-6x)-5*250x^2=0

We add all the numbers together, and all the variables

127x+(-6x)-5*250x^2=0

Wy multiply elements

-1250x^2+127x+(-6x)=0

We get rid of parentheses

-1250x^2+127x-6x=0

We add all the numbers together, and all the variables

-1250x^2+121x=0

a = -1250; b = 121; c = 0;
Δ = b2-4ac
Δ = 1212-4·(-1250)·0
Δ = 14641
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14641}=121$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(121)-121}{2*-1250}=\frac{-242}{-2500}
=121/1250
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(121)+121}{2*-1250}=\frac{0}{-2500}
=0
$