38/48x+50=x

Solution for 38/48x+50=x equation:

38/48x+50=x

We move all terms to the left:

38/48x+50-(x)=0


Domain of the equation: 48x!=0

x!=0/48

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+38/48x+50=0

We multiply all the terms by the denominator


-1x*48x+50*48x+38=0

Wy multiply elements

-48x^2+2400x+38=0

a = -48; b = 2400; c = +38;
Δ = b2-4ac
Δ = 24002-4·(-48)·38
Δ = 5767296
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:

$\sqrt{\Delta}=\sqrt{5767296}=\sqrt{64*90114}=\sqrt{64}*\sqrt{90114}=8\sqrt{90114}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2400)-8\sqrt{90114}}{2*-48}=\frac{-2400-8\sqrt{90114}}{-96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2400)+8\sqrt{90114}}{2*-48}=\frac{-2400+8\sqrt{90114}}{-96}
$