1/3x+x=800

Solution for 1/3x+x=800 equation:

1/3x+x=800

We move all terms to the left:

1/3x+x-(800)=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+1/3x-800=0

We multiply all the terms by the denominator


x*3x-800*3x+1=0

Wy multiply elements

3x^2-2400x+1=0

a = 3; b = -2400; c = +1;
Δ = b2-4ac
Δ = -24002-4·3·1
Δ = 5759988
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:

$\sqrt{\Delta}=\sqrt{5759988}=\sqrt{4*1439997}=\sqrt{4}*\sqrt{1439997}=2\sqrt{1439997}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2400)-2\sqrt{1439997}}{2*3}=\frac{2400-2\sqrt{1439997}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2400)+2\sqrt{1439997}}{2*3}=\frac{2400+2\sqrt{1439997}}{6}
$