x+5/3x=800

Solution for x+5/3x=800 equation:

x+5/3x=800

We move all terms to the left:

x+5/3x-(800)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


x*3x-800*3x+5=0

Wy multiply elements

3x^2-2400x+5=0

a = 3; b = -2400; c = +5;
Δ = b2-4ac
Δ = -24002-4·3·5
Δ = 5759940
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:

$\sqrt{\Delta}=\sqrt{5759940}=\sqrt{4*1439985}=\sqrt{4}*\sqrt{1439985}=2\sqrt{1439985}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2400)-2\sqrt{1439985}}{2*3}=\frac{2400-2\sqrt{1439985}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2400)+2\sqrt{1439985}}{2*3}=\frac{2400+2\sqrt{1439985}}{6}
$