3/8x+35=x

Solution for 3/8x+35=x equation:

3/8x+35=x

We move all terms to the left:

3/8x+35-(x)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+3/8x+35=0

We multiply all the terms by the denominator


-1x*8x+35*8x+3=0

Wy multiply elements

-8x^2+280x+3=0

a = -8; b = 280; c = +3;
Δ = b2-4ac
Δ = 2802-4·(-8)·3
Δ = 78496
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:

$\sqrt{\Delta}=\sqrt{78496}=\sqrt{16*4906}=\sqrt{16}*\sqrt{4906}=4\sqrt{4906}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(280)-4\sqrt{4906}}{2*-8}=\frac{-280-4\sqrt{4906}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(280)+4\sqrt{4906}}{2*-8}=\frac{-280+4\sqrt{4906}}{-16}
$