3/4x+x=6000

Solution for 3/4x+x=6000 equation:

3/4x+x=6000

We move all terms to the left:

3/4x+x-(6000)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

x+3/4x-6000=0

We multiply all the terms by the denominator


x*4x-6000*4x+3=0

Wy multiply elements

4x^2-24000x+3=0

a = 4; b = -24000; c = +3;
Δ = b2-4ac
Δ = -240002-4·4·3
Δ = 575999952
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:

$\sqrt{\Delta}=\sqrt{575999952}=\sqrt{16*35999997}=\sqrt{16}*\sqrt{35999997}=4\sqrt{35999997}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24000)-4\sqrt{35999997}}{2*4}=\frac{24000-4\sqrt{35999997}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24000)+4\sqrt{35999997}}{2*4}=\frac{24000+4\sqrt{35999997}}{8}
$