5x-90+x+30+1/6x+55=180

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Solution for 5x-90+x+30+1/6x+55=180 equation: 



5x-90+x+30+1/6x+55=180

We move all terms to the left:

5x-90+x+30+1/6x+55-(180)=0



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



We add all the numbers together, and all the variables

6x+1/6x-185=0

We multiply all the terms by the denominator


6x*6x-185*6x+1=0

Wy multiply elements

36x^2-1110x+1=0

a = 36; b = -1110; c = +1;
Δ = b2-4ac
Δ = -11102-4·36·1
Δ = 1231956
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:


$\sqrt{\Delta}=\sqrt{1231956}=\sqrt{36*34221}=\sqrt{36}*\sqrt{34221}=6\sqrt{34221}$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1110)-6\sqrt{34221}}{2*36}=\frac{1110-6\sqrt{34221}}{72}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1110)+6\sqrt{34221}}{2*36}=\frac{1110+6\sqrt{34221}}{72}
$

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