9-1/4x=13-2/3x

Solution for 9-1/4x=13-2/3x equation:

9-1/4x=13-2/3x

We move all terms to the left:

9-1/4x-(13-2/3x)=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+13)+9=0

We get rid of parentheses

-1/4x+2/3x-13+9=0

We calculate fractions


(-3x)/12x^2+8x/12x^2-13+9=0

We add all the numbers together, and all the variables

(-3x)/12x^2+8x/12x^2-4=0

We multiply all the terms by the denominator


(-3x)+8x-4*12x^2=0

We add all the numbers together, and all the variables

8x+(-3x)-4*12x^2=0

Wy multiply elements

-48x^2+8x+(-3x)=0

We get rid of parentheses

-48x^2+8x-3x=0

We add all the numbers together, and all the variables

-48x^2+5x=0

a = -48; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-48)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-48}=\frac{-10}{-96}
=5/48
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-48}=\frac{0}{-96}
=0
$