200/1.5x+5=x

Solution for 200/1.5x+5=x equation:

200/1.5x+5=x

We move all terms to the left:

200/1.5x+5-(x)=0


Domain of the equation: 1.5x!=0

x!=0/1.5

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+200/1.5x+5=0

We multiply all the terms by the denominator


-1x*1.5x+5*1.5x+200=0

Wy multiply elements

-1x^2+5x+200=0

a = -1; b = 5; c = +200;
Δ = b2-4ac
Δ = 52-4·(-1)·200
Δ = 825
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:

$\sqrt{\Delta}=\sqrt{825}=\sqrt{25*33}=\sqrt{25}*\sqrt{33}=5\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5\sqrt{33}}{2*-1}=\frac{-5-5\sqrt{33}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5\sqrt{33}}{2*-1}=\frac{-5+5\sqrt{33}}{-2}
$