(2/3x)+1=x-4

Solution for (2/3x)+1=x-4 equation:

(2/3x)+1=x-4

We move all terms to the left:

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


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-3x^2+12x+3x+2=0

We add all the numbers together, and all the variables

-3x^2+15x+2=0

a = -3; b = 15; c = +2;
Δ = b2-4ac
Δ = 152-4·(-3)·2
Δ = 249
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{-(15)-\sqrt{249}}{2*-3}=\frac{-15-\sqrt{249}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{249}}{2*-3}=\frac{-15+\sqrt{249}}{-6}
$