x=6-3/4x

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

x=6-3/4x

We move all terms to the left:

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


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

x+3/4x-6=0

We multiply all the terms by the denominator


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

Wy multiply elements

4x^2-24x+3=0

a = 4; b = -24; c = +3;
Δ = b2-4ac
Δ = -242-4·4·3
Δ = 528
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:

$\sqrt{\Delta}=\sqrt{528}=\sqrt{16*33}=\sqrt{16}*\sqrt{33}=4\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{33}}{2*4}=\frac{24-4\sqrt{33}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{33}}{2*4}=\frac{24+4\sqrt{33}}{8}
$