2*3x-4=4*1/2x-8

Solution for 2*3x-4=4*1/2x-8 equation:

2*3x-4=4*1/2x-8

We move all terms to the left:

2*3x-4-(4*1/2x-8)=0


Domain of the equation: 2x-8)!=0

x∈R


Wy multiply elements

6x-(4*1/2x-8)-4=0

We get rid of parentheses

6x-4*1/2x+8-4=0

We multiply all the terms by the denominator


6x*2x+8*2x-4*2x-4*1=0

We add all the numbers together, and all the variables

6x*2x+8*2x-4*2x-4=0

Wy multiply elements

12x^2+16x-8x-4=0

We add all the numbers together, and all the variables

12x^2+8x-4=0

a = 12; b = 8; c = -4;
Δ = b2-4ac
Δ = 82-4·12·(-4)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-16}{2*12}=\frac{-24}{24}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+16}{2*12}=\frac{8}{24}
=1/3
$