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5/6a+a=125
We move all terms to the left:
5/6a+a-(125)=0
Domain of the equation: 6a!=0We add all the numbers together, and all the variables
a!=0/6
a!=0
a∈R
a+5/6a-125=0
We multiply all the terms by the denominator
a*6a-125*6a+5=0
Wy multiply elements
6a^2-750a+5=0
a = 6; b = -750; c = +5;
Δ = b2-4ac
Δ = -7502-4·6·5
Δ = 562380
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}$$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{562380}=\sqrt{4*140595}=\sqrt{4}*\sqrt{140595}=2\sqrt{140595}$$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-750)-2\sqrt{140595}}{2*6}=\frac{750-2\sqrt{140595}}{12} $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-750)+2\sqrt{140595}}{2*6}=\frac{750+2\sqrt{140595}}{12} $
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