1/4x-5=7-2/3x

Solution for 1/4x-5=7-2/3x equation:

1/4x-5=7-2/3x

We move all terms to the left:

1/4x-5-(7-2/3x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/4x-(-2/3x+7)-5=0

We get rid of parentheses

1/4x+2/3x-7-5=0

We calculate fractions


3x/12x^2+8x/12x^2-7-5=0

We add all the numbers together, and all the variables

3x/12x^2+8x/12x^2-12=0

We multiply all the terms by the denominator


3x+8x-12*12x^2=0

We add all the numbers together, and all the variables

11x-12*12x^2=0

Wy multiply elements

-144x^2+11x=0

a = -144; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-144)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-144}=\frac{-22}{-288}
=11/144
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-144}=\frac{0}{-288}
=0
$