1/2x-4/5=3/5x+1

Solution for 1/2x-4/5=3/5x+1 equation:

1/2x-4/5=3/5x+1

We move all terms to the left:

1/2x-4/5-(3/5x+1)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 5x+1)!=0

x∈R


We get rid of parentheses

1/2x-3/5x-1-4/5=0

We calculate fractions


125x/250x^2+(-6x)/250x^2+(-8x)/250x^2-1=0

We multiply all the terms by the denominator


125x+(-6x)+(-8x)-1*250x^2=0

Wy multiply elements

-250x^2+125x+(-6x)+(-8x)=0

We get rid of parentheses

-250x^2+125x-6x-8x=0

We add all the numbers together, and all the variables

-250x^2+111x=0

a = -250; b = 111; c = 0;
Δ = b2-4ac
Δ = 1112-4·(-250)·0
Δ = 12321
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12321}=111$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(111)-111}{2*-250}=\frac{-222}{-500}
=111/250
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(111)+111}{2*-250}=\frac{0}{-500}
=0
$