3/4x+600=x

Solution for 3/4x+600=x equation:

3/4x+600=x

We move all terms to the left:

3/4x+600-(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+3/4x+600=0

We multiply all the terms by the denominator


-1x*4x+600*4x+3=0

Wy multiply elements

-4x^2+2400x+3=0

a = -4; b = 2400; c = +3;
Δ = b2-4ac
Δ = 24002-4·(-4)·3
Δ = 5760048
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:

$\sqrt{\Delta}=\sqrt{5760048}=\sqrt{784*7347}=\sqrt{784}*\sqrt{7347}=28\sqrt{7347}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2400)-28\sqrt{7347}}{2*-4}=\frac{-2400-28\sqrt{7347}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2400)+28\sqrt{7347}}{2*-4}=\frac{-2400+28\sqrt{7347}}{-8}
$