3/4x-x=-500

Solution for 3/4x-x=-500 equation:

3/4x-x=-500

We move all terms to the left:

3/4x-x-(-500)=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+3/4x+500=0

We multiply all the terms by the denominator


-1x*4x+500*4x+3=0

Wy multiply elements

-4x^2+2000x+3=0

a = -4; b = 2000; c = +3;
Δ = b2-4ac
Δ = 20002-4·(-4)·3
Δ = 4000048
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:

$\sqrt{\Delta}=\sqrt{4000048}=\sqrt{16*250003}=\sqrt{16}*\sqrt{250003}=4\sqrt{250003}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2000)-4\sqrt{250003}}{2*-4}=\frac{-2000-4\sqrt{250003}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2000)+4\sqrt{250003}}{2*-4}=\frac{-2000+4\sqrt{250003}}{-8}
$