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5a-2/2a-11=2
We move all terms to the left:
5a-2/2a-11-(2)=0
Domain of the equation: 2a!=0We add all the numbers together, and all the variables
a!=0/2
a!=0
a∈R
5a-2/2a-13=0
We multiply all the terms by the denominator
5a*2a-13*2a-2=0
Wy multiply elements
10a^2-26a-2=0
a = 10; b = -26; c = -2;
Δ = b2-4ac
Δ = -262-4·10·(-2)
Δ = 756
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}$$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{756}=\sqrt{36*21}=\sqrt{36}*\sqrt{21}=6\sqrt{21}$$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-6\sqrt{21}}{2*10}=\frac{26-6\sqrt{21}}{20} $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+6\sqrt{21}}{2*10}=\frac{26+6\sqrt{21}}{20} $
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