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

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

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

We move all terms to the left:

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


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

x∈R


We add all the numbers together, and all the variables

-0.5x-(1/3x-4)+1=0

We get rid of parentheses

-0.5x-1/3x+4+1=0

We multiply all the terms by the denominator


-(0.5x)*3x+4*3x+1*3x-1=0

We add all the numbers together, and all the variables

-(+0.5x)*3x+4*3x+1*3x-1=0

We multiply parentheses

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

Wy multiply elements

-0x^2+12x+3x-1=0

We add all the numbers together, and all the variables

-1x^2+15x-1=0

a = -1; b = 15; c = -1;
Δ = b2-4ac
Δ = 152-4·(-1)·(-1)
Δ = 221
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{221}}{2*-1}=\frac{-15-\sqrt{221}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{221}}{2*-1}=\frac{-15+\sqrt{221}}{-2}
$