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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 4x+1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


80x^2/180x^2+144x/180x^2+(-135x)/180x^2-1=0

We multiply all the terms by the denominator


80x^2+144x+(-135x)-1*180x^2=0

Wy multiply elements

80x^2-180x^2+144x+(-135x)=0

We get rid of parentheses

80x^2-180x^2+144x-135x=0

We add all the numbers together, and all the variables

-100x^2+9x=0

a = -100; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-100)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-100}=\frac{-18}{-200}
=9/100
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-100}=\frac{0}{-200}
=0
$