X=39-3/4x

Solution for X=39-3/4x equation:

X=39-3/4X

We move all terms to the left:

X-(39-3/4X)=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+39)=0

We get rid of parentheses

X+3/4X-39=0

We multiply all the terms by the denominator


X*4X-39*4X+3=0

Wy multiply elements

4X^2-156X+3=0

a = 4; b = -156; c = +3;
Δ = b2-4ac
Δ = -1562-4·4·3
Δ = 24288
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:

$\sqrt{\Delta}=\sqrt{24288}=\sqrt{16*1518}=\sqrt{16}*\sqrt{1518}=4\sqrt{1518}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-156)-4\sqrt{1518}}{2*4}=\frac{156-4\sqrt{1518}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-156)+4\sqrt{1518}}{2*4}=\frac{156+4\sqrt{1518}}{8}
$