3/4x=0.25x+250

Solution for 3/4x=0.25x+250 equation:

3/4x=0.25x+250

We move all terms to the left:

3/4x-(0.25x+250)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

3/4x-0.25x-250=0

We multiply all the terms by the denominator


-(0.25x)*4x-250*4x+3=0

We add all the numbers together, and all the variables

-(+0.25x)*4x-250*4x+3=0

We multiply parentheses

-0x^2-250*4x+3=0

Wy multiply elements

-0x^2-1000x+3=0

We add all the numbers together, and all the variables

-1x^2-1000x+3=0

a = -1; b = -1000; c = +3;
Δ = b2-4ac
Δ = -10002-4·(-1)·3
Δ = 1000012
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:

$\sqrt{\Delta}=\sqrt{1000012}=\sqrt{4*250003}=\sqrt{4}*\sqrt{250003}=2\sqrt{250003}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1000)-2\sqrt{250003}}{2*-1}=\frac{1000-2\sqrt{250003}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1000)+2\sqrt{250003}}{2*-1}=\frac{1000+2\sqrt{250003}}{-2}
$