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

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

X+5/4=1-X/3X-4

We move all terms to the left:

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


Domain of the equation: 3X-4)!=0

X∈R


We add all the numbers together, and all the variables

X-(-X/3X-3)+5/4=0

We get rid of parentheses

X+X/3X+3+5/4=0

We calculate fractions


X+4X/12X+15X/12X+3=0

We multiply all the terms by the denominator


X*12X+4X+15X+3*12X=0

We add all the numbers together, and all the variables

19X+X*12X+3*12X=0

Wy multiply elements

12X^2+19X+36X=0

We add all the numbers together, and all the variables

12X^2+55X=0

a = 12; b = 55; c = 0;
Δ = b2-4ac
Δ = 552-4·12·0
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(55)-55}{2*12}=\frac{-110}{24}
=-4+7/12
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+55}{2*12}=\frac{0}{24}
=0
$