5/4x+800=x

Solution for 5/4x+800=x equation:

5/4x+800=x

We move all terms to the left:

5/4x+800-(x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+5/4x+800=0

We multiply all the terms by the denominator


-1x*4x+800*4x+5=0

Wy multiply elements

-4x^2+3200x+5=0

a = -4; b = 3200; c = +5;
Δ = b2-4ac
Δ = 32002-4·(-4)·5
Δ = 10240080
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:

$\sqrt{\Delta}=\sqrt{10240080}=\sqrt{16*640005}=\sqrt{16}*\sqrt{640005}=4\sqrt{640005}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3200)-4\sqrt{640005}}{2*-4}=\frac{-3200-4\sqrt{640005}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3200)+4\sqrt{640005}}{2*-4}=\frac{-3200+4\sqrt{640005}}{-8}
$