-3x+8=x-3x+6-1/2*2x-4

Solution for -3x+8=x-3x+6-1/2*2x-4 equation:

-3x+8=x-3x+6-1/2*2x-4

We move all terms to the left:

-3x+8-(x-3x+6-1/2*2x-4)=0


Domain of the equation: 2*2x-4)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

-3x+2x+1/2*2x-2+8=0

We multiply all the terms by the denominator


-3x*2*2x+2x*2*2x-2*2*2x+8*2*2x+1=0

Wy multiply elements

-12x^2*2+8x^2*2-8x*2+32x*2+1=0

Wy multiply elements

-24x^2+16x^2-16x+64x+1=0

We add all the numbers together, and all the variables

-8x^2+48x+1=0

a = -8; b = 48; c = +1;
Δ = b2-4ac
Δ = 482-4·(-8)·1
Δ = 2336
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:

$\sqrt{\Delta}=\sqrt{2336}=\sqrt{16*146}=\sqrt{16}*\sqrt{146}=4\sqrt{146}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-4\sqrt{146}}{2*-8}=\frac{-48-4\sqrt{146}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+4\sqrt{146}}{2*-8}=\frac{-48+4\sqrt{146}}{-16}
$