X+1/3x=2700

Solution for X+1/3x=2700 equation:

X+1/3X=2700

We move all terms to the left:

X+1/3X-(2700)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We multiply all the terms by the denominator


X*3X-2700*3X+1=0

Wy multiply elements

3X^2-8100X+1=0

a = 3; b = -8100; c = +1;
Δ = b2-4ac
Δ = -81002-4·3·1
Δ = 65609988
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:

$\sqrt{\Delta}=\sqrt{65609988}=\sqrt{4*16402497}=\sqrt{4}*\sqrt{16402497}=2\sqrt{16402497}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8100)-2\sqrt{16402497}}{2*3}=\frac{8100-2\sqrt{16402497}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8100)+2\sqrt{16402497}}{2*3}=\frac{8100+2\sqrt{16402497}}{6}
$