7/10x-2=2/5x-1

Solution for 7/10x-2=2/5x-1 equation:

7/10x-2=2/5x-1

We move all terms to the left:

7/10x-2-(2/5x-1)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R



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

x∈R


We get rid of parentheses

7/10x-2/5x+1-2=0

We calculate fractions


35x/50x^2+(-20x)/50x^2+1-2=0

We add all the numbers together, and all the variables

35x/50x^2+(-20x)/50x^2-1=0

We multiply all the terms by the denominator


35x+(-20x)-1*50x^2=0

Wy multiply elements

-50x^2+35x+(-20x)=0

We get rid of parentheses

-50x^2+35x-20x=0

We add all the numbers together, and all the variables

-50x^2+15x=0

a = -50; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·(-50)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*-50}=\frac{-30}{-100}
=3/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*-50}=\frac{0}{-100}
=0
$