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

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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 get rid of parentheses

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

We multiply all the terms by the denominator


x*3x+3x*3x-14*3x+7*3x-73*3x-180*3x+1=0

Wy multiply elements

3x^2+9x^2-42x+21x-219x-540x+1=0

We add all the numbers together, and all the variables

12x^2-780x+1=0

a = 12; b = -780; c = +1;
Δ = b2-4ac
Δ = -7802-4·12·1
Δ = 608352
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:


$\sqrt{\Delta}=\sqrt{608352}=\sqrt{16*38022}=\sqrt{16}*\sqrt{38022}=4\sqrt{38022}$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-780)-4\sqrt{38022}}{2*12}=\frac{780-4\sqrt{38022}}{24}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-780)+4\sqrt{38022}}{2*12}=\frac{780+4\sqrt{38022}}{24}
$

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