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

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

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

We move all terms to the left:

1/2x+-3/5-(3/5x-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 add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

1250x^2+125x+(-6x)+(-6x)=0

We get rid of parentheses

1250x^2+125x-6x-6x=0

We add all the numbers together, and all the variables

1250x^2+113x=0

a = 1250; b = 113; c = 0;
Δ = b2-4ac
Δ = 1132-4·1250·0
Δ = 12769
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12769}=113$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(113)-113}{2*1250}=\frac{-226}{2500}
=-113/1250
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(113)+113}{2*1250}=\frac{0}{2500}
=0
$