4*1/3x-x+5=2x-6

Solution for 4*1/3x-x+5=2x-6 equation:

4*1/3x-x+5=2x-6

We move all terms to the left:

4*1/3x-x+5-(2x-6)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+4*1/3x-(2x-6)+5=0

We get rid of parentheses

-1x+4*1/3x-2x+6+5=0

We multiply all the terms by the denominator


-1x*3x-2x*3x+6*3x+5*3x+4*1=0

We add all the numbers together, and all the variables

-1x*3x-2x*3x+6*3x+5*3x+4=0

Wy multiply elements

-3x^2-6x^2+18x+15x+4=0

We add all the numbers together, and all the variables

-9x^2+33x+4=0

a = -9; b = 33; c = +4;
Δ = b2-4ac
Δ = 332-4·(-9)·4
Δ = 1233
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1233}=\sqrt{9*137}=\sqrt{9}*\sqrt{137}=3\sqrt{137}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-3\sqrt{137}}{2*-9}=\frac{-33-3\sqrt{137}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+3\sqrt{137}}{2*-9}=\frac{-33+3\sqrt{137}}{-18}
$