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

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

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

We move all terms to the left:

2/3x-4-(-1+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

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-15x^2+3x-12x+2=0

We add all the numbers together, and all the variables

-15x^2-9x+2=0

a = -15; b = -9; c = +2;
Δ = b2-4ac
Δ = -92-4·(-15)·2
Δ = 201
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{-(-9)-\sqrt{201}}{2*-15}=\frac{9-\sqrt{201}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{201}}{2*-15}=\frac{9+\sqrt{201}}{-30}
$