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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


4x/12x^2+15x/12x^2-4-3=0

We add all the numbers together, and all the variables

4x/12x^2+15x/12x^2-7=0

We multiply all the terms by the denominator


4x+15x-7*12x^2=0

We add all the numbers together, and all the variables

19x-7*12x^2=0

Wy multiply elements

-84x^2+19x=0

a = -84; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·(-84)·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-19}{2*-84}=\frac{-38}{-168}
=19/84
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*-84}=\frac{0}{-168}
=0
$