31/3x-4.5=11x+4.5-2.5x

Solution for 31/3x-4.5=11x+4.5-2.5x equation:

31/3x-4.5=11x+4.5-2.5x

We move all terms to the left:

31/3x-4.5-(11x+4.5-2.5x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

31/3x-(8.5x+4.5)-4.5=0

We get rid of parentheses

31/3x-8.5x-4.5-4.5=0

We multiply all the terms by the denominator


-(8.5x)*3x-(4.5)*3x-(4.5)*3x+31=0

We add all the numbers together, and all the variables

-(+8.5x)*3x-(4.5)*3x-(4.5)*3x+31=0

We multiply parentheses

-24x^2-13.5x-13.5x+31=0

We add all the numbers together, and all the variables

-24x^2-27x+31=0

a = -24; b = -27; c = +31;
Δ = b2-4ac
Δ = -272-4·(-24)·31
Δ = 3705
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-\sqrt{3705}}{2*-24}=\frac{27-\sqrt{3705}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{3705}}{2*-24}=\frac{27+\sqrt{3705}}{-48}
$