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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x-1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-150x^2)/800x^2+640x/800x^2+(-240x)/800x^2+1=0

We multiply all the terms by the denominator


(-150x^2)+640x+(-240x)+1*800x^2=0

Wy multiply elements

(-150x^2)+800x^2+640x+(-240x)=0

We get rid of parentheses

-150x^2+800x^2+640x-240x=0

We add all the numbers together, and all the variables

650x^2+400x=0

a = 650; b = 400; c = 0;
Δ = b2-4ac
Δ = 4002-4·650·0
Δ = 160000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{160000}=400$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(400)-400}{2*650}=\frac{-800}{1300}
=-8/13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(400)+400}{2*650}=\frac{0}{1300}
=0
$