3/4x-2=6-2x

Solution for 3/4x-2=6-2x equation:

3/4x-2=6-2x

We move all terms to the left:

3/4x-2-(6-2x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

3/4x+2x-6-2=0

We multiply all the terms by the denominator


2x*4x-6*4x-2*4x+3=0

Wy multiply elements

8x^2-24x-8x+3=0

We add all the numbers together, and all the variables

8x^2-32x+3=0

a = 8; b = -32; c = +3;
Δ = b2-4ac
Δ = -322-4·8·3
Δ = 928
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:

$\sqrt{\Delta}=\sqrt{928}=\sqrt{16*58}=\sqrt{16}*\sqrt{58}=4\sqrt{58}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{58}}{2*8}=\frac{32-4\sqrt{58}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{58}}{2*8}=\frac{32+4\sqrt{58}}{16}
$