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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-100x^2)/200x^2+150x/200x^2+(-160x)/200x^2=0

We multiply all the terms by the denominator


(-100x^2)+150x+(-160x)=0

We get rid of parentheses

-100x^2+150x-160x=0

We add all the numbers together, and all the variables

-100x^2-10x=0

a = -100; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·(-100)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*-100}=\frac{0}{-200}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*-100}=\frac{20}{-200}
=-1/10
$