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a+1/2a+5+2a=180
We move all terms to the left:
a+1/2a+5+2a-(180)=0
Domain of the equation: 2a!=0We add all the numbers together, and all the variables
a!=0/2
a!=0
a∈R
3a+1/2a-175=0
We multiply all the terms by the denominator
3a*2a-175*2a+1=0
Wy multiply elements
6a^2-350a+1=0
a = 6; b = -350; c = +1;
Δ = b2-4ac
Δ = -3502-4·6·1
Δ = 122476
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}$$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{122476}=\sqrt{4*30619}=\sqrt{4}*\sqrt{30619}=2\sqrt{30619}$$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-350)-2\sqrt{30619}}{2*6}=\frac{350-2\sqrt{30619}}{12} $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-350)+2\sqrt{30619}}{2*6}=\frac{350+2\sqrt{30619}}{12} $
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