22/24x+3=x

Solution for 22/24x+3=x equation:

22/24x+3=x

We move all terms to the left:

22/24x+3-(x)=0


Domain of the equation: 24x!=0

x!=0/24

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+22/24x+3=0

We multiply all the terms by the denominator


-1x*24x+3*24x+22=0

Wy multiply elements

-24x^2+72x+22=0

a = -24; b = 72; c = +22;
Δ = b2-4ac
Δ = 722-4·(-24)·22
Δ = 7296
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:

$\sqrt{\Delta}=\sqrt{7296}=\sqrt{64*114}=\sqrt{64}*\sqrt{114}=8\sqrt{114}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-8\sqrt{114}}{2*-24}=\frac{-72-8\sqrt{114}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+8\sqrt{114}}{2*-24}=\frac{-72+8\sqrt{114}}{-48}
$