3/4x+1,000=6x

Solution for 3/4x+1,000=6x equation:

3/4x+1.000=6x

We move all terms to the left:

3/4x+1.000-(6x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

-6x+3/4x+1=0

We multiply all the terms by the denominator


-6x*4x+1*4x+3=0

Wy multiply elements

-24x^2+4x+3=0

a = -24; b = 4; c = +3;
Δ = b2-4ac
Δ = 42-4·(-24)·3
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{19}}{2*-24}=\frac{-4-4\sqrt{19}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{19}}{2*-24}=\frac{-4+4\sqrt{19}}{-48}
$