X+1/3y=640

Solution for X+1/3y=640 equation:

X+1/3X=640

We move all terms to the left:

X+1/3X-(640)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We multiply all the terms by the denominator


X*3X-640*3X+1=0

Wy multiply elements

3X^2-1920X+1=0

a = 3; b = -1920; c = +1;
Δ = b2-4ac
Δ = -19202-4·3·1
Δ = 3686388
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:

$\sqrt{\Delta}=\sqrt{3686388}=\sqrt{4*921597}=\sqrt{4}*\sqrt{921597}=2\sqrt{921597}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1920)-2\sqrt{921597}}{2*3}=\frac{1920-2\sqrt{921597}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1920)+2\sqrt{921597}}{2*3}=\frac{1920+2\sqrt{921597}}{6}
$