X+2/3y=120

Solution for X+2/3y=120 equation:

X+2/3X=120

We move all terms to the left:

X+2/3X-(120)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We multiply all the terms by the denominator


X*3X-120*3X+2=0

Wy multiply elements

3X^2-360X+2=0

a = 3; b = -360; c = +2;
Δ = b2-4ac
Δ = -3602-4·3·2
Δ = 129576
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:

$\sqrt{\Delta}=\sqrt{129576}=\sqrt{4*32394}=\sqrt{4}*\sqrt{32394}=2\sqrt{32394}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-2\sqrt{32394}}{2*3}=\frac{360-2\sqrt{32394}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+2\sqrt{32394}}{2*3}=\frac{360+2\sqrt{32394}}{6}
$