1/2(6a)+6a+a=180

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Solution for 1/2(6a)+6a+a=180 equation: 



1/2(6a)+6a+a=180

We move all terms to the left:

1/2(6a)+6a+a-(180)=0



Domain of the equation: 26a!=0

a!=0/26

a!=0

a∈R



We add all the numbers together, and all the variables

7a+1/26a-180=0

We multiply all the terms by the denominator


7a*26a-180*26a+1=0

Wy multiply elements

182a^2-4680a+1=0

a = 182; b = -4680; c = +1;
Δ = b2-4ac
Δ = -46802-4·182·1
Δ = 21901672
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:


$\sqrt{\Delta}=\sqrt{21901672}=\sqrt{4*5475418}=\sqrt{4}*\sqrt{5475418}=2\sqrt{5475418}$


$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4680)-2\sqrt{5475418}}{2*182}=\frac{4680-2\sqrt{5475418}}{364}
$


$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4680)+2\sqrt{5475418}}{2*182}=\frac{4680+2\sqrt{5475418}}{364}
$

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