X-1/3x+x+50=360

Solution for X-1/3x+x+50=360 equation:

X-1/3X+X+50=360

We move all terms to the left:

X-1/3X+X+50-(360)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We add all the numbers together, and all the variables

2X-1/3X-310=0

We multiply all the terms by the denominator


2X*3X-310*3X-1=0

Wy multiply elements

6X^2-930X-1=0

a = 6; b = -930; c = -1;
Δ = b2-4ac
Δ = -9302-4·6·(-1)
Δ = 864924
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:

$\sqrt{\Delta}=\sqrt{864924}=\sqrt{4*216231}=\sqrt{4}*\sqrt{216231}=2\sqrt{216231}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-930)-2\sqrt{216231}}{2*6}=\frac{930-2\sqrt{216231}}{12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-930)+2\sqrt{216231}}{2*6}=\frac{930+2\sqrt{216231}}{12}
$