1/3x+(2x-30)-40=360

Solution for 1/3x+(2x-30)-40=360 equation:

1/3x+(2x-30)-40=360

We move all terms to the left:

1/3x+(2x-30)-40-(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

1/3x+(2x-30)-400=0

We get rid of parentheses

1/3x+2x-30-400=0

We multiply all the terms by the denominator


2x*3x-30*3x-400*3x+1=0

Wy multiply elements

6x^2-90x-1200x+1=0

We add all the numbers together, and all the variables

6x^2-1290x+1=0

a = 6; b = -1290; c = +1;
Δ = b2-4ac
Δ = -12902-4·6·1
Δ = 1664076
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:

$\sqrt{\Delta}=\sqrt{1664076}=\sqrt{4*416019}=\sqrt{4}*\sqrt{416019}=2\sqrt{416019}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1290)-2\sqrt{416019}}{2*6}=\frac{1290-2\sqrt{416019}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1290)+2\sqrt{416019}}{2*6}=\frac{1290+2\sqrt{416019}}{12}
$