1-3/(5x)=4/(10x)

Solution for 1-3/(5x)=4/(10x) equation:

1-3/(5x)=4/(10x)

We move all terms to the left:

1-3/(5x)-(4/(10x))=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-3/5x-(+4/10x)+1=0

We get rid of parentheses

-3/5x-4/10x+1=0

We calculate fractions


(-30x)/50x^2+(-20x)/50x^2+1=0

We multiply all the terms by the denominator


(-30x)+(-20x)+1*50x^2=0

Wy multiply elements

50x^2+(-30x)+(-20x)=0

We get rid of parentheses

50x^2-30x-20x=0

We add all the numbers together, and all the variables

50x^2-50x=0

a = 50; b = -50; c = 0;
Δ = b2-4ac
Δ = -502-4·50·0
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-50}{2*50}=\frac{0}{100}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+50}{2*50}=\frac{100}{100}
=1
$