x-28+2x-106+(1/3x)+14=180

Solution for x-28+2x-106+(1/3x)+14=180 equation:

x-28+2x-106+(1/3x)+14=180

We move all terms to the left:

x-28+2x-106+(1/3x)+14-(180)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x+2x+(+1/3x)-28-106+14-180=0

We add all the numbers together, and all the variables

3x+(+1/3x)-300=0

We get rid of parentheses

3x+1/3x-300=0

We multiply all the terms by the denominator


3x*3x-300*3x+1=0

Wy multiply elements

9x^2-900x+1=0

a = 9; b = -900; c = +1;
Δ = b2-4ac
Δ = -9002-4·9·1
Δ = 809964
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:

$\sqrt{\Delta}=\sqrt{809964}=\sqrt{36*22499}=\sqrt{36}*\sqrt{22499}=6\sqrt{22499}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-900)-6\sqrt{22499}}{2*9}=\frac{900-6\sqrt{22499}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-900)+6\sqrt{22499}}{2*9}=\frac{900+6\sqrt{22499}}{18}
$