(x-14)+(1/3x+7)+3x-73)=180

Solution for (x-14)+(1/3x+7)+3x-73)=180 equation:

(x-14)+(1/3x+7)+3x-73)=180

We move all terms to the left:

(x-14)+(1/3x+7)+3x-73)-(180)=0


Domain of the equation: 3x+7)!=0

x∈R


We add all the numbers together, and all the variables

3x+(x-14)+(1/3x+7)=0

We get rid of parentheses

3x+x+1/3x-14+7=0

We multiply all the terms by the denominator


3x*3x+x*3x-14*3x+7*3x+1=0

Wy multiply elements

9x^2+3x^2-42x+21x+1=0

We add all the numbers together, and all the variables

12x^2-21x+1=0

a = 12; b = -21; c = +1;
Δ = b2-4ac
Δ = -212-4·12·1
Δ = 393
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-\sqrt{393}}{2*12}=\frac{21-\sqrt{393}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{393}}{2*12}=\frac{21+\sqrt{393}}{24}
$