x=1/4x+860,000

Solution for x=1/4x+860,000 equation:

x=1/4x+860.000

We move all terms to the left:

x-(1/4x+860.000)=0


Domain of the equation: 4x+860.000)!=0

x∈R


We add all the numbers together, and all the variables

x-(1/4x+860)=0

We get rid of parentheses

x-1/4x-860=0

We multiply all the terms by the denominator


x*4x-860*4x-1=0

Wy multiply elements

4x^2-3440x-1=0

a = 4; b = -3440; c = -1;
Δ = b2-4ac
Δ = -34402-4·4·(-1)
Δ = 11833616
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:

$\sqrt{\Delta}=\sqrt{11833616}=\sqrt{16*739601}=\sqrt{16}*\sqrt{739601}=4\sqrt{739601}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3440)-4\sqrt{739601}}{2*4}=\frac{3440-4\sqrt{739601}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3440)+4\sqrt{739601}}{2*4}=\frac{3440+4\sqrt{739601}}{8}
$