1/3x+20x+10x+40=360

Solution for 1/3x+20x+10x+40=360 equation:

1/3x+20x+10x+40=360

We move all terms to the left:

1/3x+20x+10x+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

30x+1/3x-320=0

We multiply all the terms by the denominator


30x*3x-320*3x+1=0

Wy multiply elements

90x^2-960x+1=0

a = 90; b = -960; c = +1;
Δ = b2-4ac
Δ = -9602-4·90·1
Δ = 921240
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:

$\sqrt{\Delta}=\sqrt{921240}=\sqrt{36*25590}=\sqrt{36}*\sqrt{25590}=6\sqrt{25590}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-960)-6\sqrt{25590}}{2*90}=\frac{960-6\sqrt{25590}}{180}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-960)+6\sqrt{25590}}{2*90}=\frac{960+6\sqrt{25590}}{180}
$