3/8x+30=x

Solution for 3/8x+30=x equation:

3/8x+30=x

We move all terms to the left:

3/8x+30-(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+30=0

We multiply all the terms by the denominator


-1x*8x+30*8x+3=0

Wy multiply elements

-8x^2+240x+3=0

a = -8; b = 240; c = +3;
Δ = b2-4ac
Δ = 2402-4·(-8)·3
Δ = 57696
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:

$\sqrt{\Delta}=\sqrt{57696}=\sqrt{16*3606}=\sqrt{16}*\sqrt{3606}=4\sqrt{3606}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(240)-4\sqrt{3606}}{2*-8}=\frac{-240-4\sqrt{3606}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(240)+4\sqrt{3606}}{2*-8}=\frac{-240+4\sqrt{3606}}{-16}
$