12+x+36+1/6x+56=180

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Solution for 12+x+36+1/6x+56=180 equation: 



12+x+36+1/6x+56=180

We move all terms to the left:

12+x+36+1/6x+56-(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

x+1/6x-76=0

We multiply all the terms by the denominator


x*6x-76*6x+1=0

Wy multiply elements

6x^2-456x+1=0

a = 6; b = -456; c = +1;
Δ = b2-4ac
Δ = -4562-4·6·1
Δ = 207912
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:


$\sqrt{\Delta}=\sqrt{207912}=\sqrt{4*51978}=\sqrt{4}*\sqrt{51978}=2\sqrt{51978}$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-456)-2\sqrt{51978}}{2*6}=\frac{456-2\sqrt{51978}}{12}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-456)+2\sqrt{51978}}{2*6}=\frac{456+2\sqrt{51978}}{12}
$

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