5/3x+x=400

Solution for 5/3x+x=400 equation:

5/3x+x=400

We move all terms to the left:

5/3x+x-(400)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

x+5/3x-400=0

We multiply all the terms by the denominator


x*3x-400*3x+5=0

Wy multiply elements

3x^2-1200x+5=0

a = 3; b = -1200; c = +5;
Δ = b2-4ac
Δ = -12002-4·3·5
Δ = 1439940
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:

$\sqrt{\Delta}=\sqrt{1439940}=\sqrt{4*359985}=\sqrt{4}*\sqrt{359985}=2\sqrt{359985}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1200)-2\sqrt{359985}}{2*3}=\frac{1200-2\sqrt{359985}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1200)+2\sqrt{359985}}{2*3}=\frac{1200+2\sqrt{359985}}{6}
$