1/4x+3/5=9+2/3x

Solution for 1/4x+3/5=9+2/3x equation:

1/4x+3/5=9+2/3x

We move all terms to the left:

1/4x+3/5-(9+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+9)+3/5=0

We get rid of parentheses

1/4x-2/3x-9+3/5=0

We calculate fractions


108x^2/300x^2+75x/300x^2+(-200x)/300x^2-9=0

We multiply all the terms by the denominator


108x^2+75x+(-200x)-9*300x^2=0

Wy multiply elements

108x^2-2700x^2+75x+(-200x)=0

We get rid of parentheses

108x^2-2700x^2+75x-200x=0

We add all the numbers together, and all the variables

-2592x^2-125x=0

a = -2592; b = -125; c = 0;
Δ = b2-4ac
Δ = -1252-4·(-2592)·0
Δ = 15625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{15625}=125$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-125)-125}{2*-2592}=\frac{0}{-5184}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-125)+125}{2*-2592}=\frac{250}{-5184}
=-125/2592
$