-x+4=5/3x-4

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

-x+4=5/3x-4

We move all terms to the left:

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


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

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-3x^2+12x+12x-5=0

We add all the numbers together, and all the variables

-3x^2+24x-5=0

a = -3; b = 24; c = -5;
Δ = b2-4ac
Δ = 242-4·(-3)·(-5)
Δ = 516
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:

$\sqrt{\Delta}=\sqrt{516}=\sqrt{4*129}=\sqrt{4}*\sqrt{129}=2\sqrt{129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{129}}{2*-3}=\frac{-24-2\sqrt{129}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{129}}{2*-3}=\frac{-24+2\sqrt{129}}{-6}
$