3/4x+102=x

Solution for 3/4x+102=x equation:

3/4x+102=x

We move all terms to the left:

3/4x+102-(x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+3/4x+102=0

We multiply all the terms by the denominator


-1x*4x+102*4x+3=0

Wy multiply elements

-4x^2+408x+3=0

a = -4; b = 408; c = +3;
Δ = b2-4ac
Δ = 4082-4·(-4)·3
Δ = 166512
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:

$\sqrt{\Delta}=\sqrt{166512}=\sqrt{16*10407}=\sqrt{16}*\sqrt{10407}=4\sqrt{10407}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(408)-4\sqrt{10407}}{2*-4}=\frac{-408-4\sqrt{10407}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(408)+4\sqrt{10407}}{2*-4}=\frac{-408+4\sqrt{10407}}{-8}
$