x-4=3/4x-2

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

x-4=3/4x-2

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

4x^2+8x-16x-3=0

We add all the numbers together, and all the variables

4x^2-8x-3=0

a = 4; b = -8; c = -3;
Δ = b2-4ac
Δ = -82-4·4·(-3)
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{7}}{2*4}=\frac{8-4\sqrt{7}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{7}}{2*4}=\frac{8+4\sqrt{7}}{8}
$