41/2a+31/4a=217

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Solution for 41/2a+31/4a=217 equation:



41/2a+31/4a=217
We move all terms to the left:
41/2a+31/4a-(217)=0
Domain of the equation: 2a!=0
a!=0/2
a!=0
a∈R
Domain of the equation: 4a!=0
a!=0/4
a!=0
a∈R
We calculate fractions
164a/8a^2+62a/8a^2-217=0
We multiply all the terms by the denominator
164a+62a-217*8a^2=0
We add all the numbers together, and all the variables
226a-217*8a^2=0
Wy multiply elements
-1736a^2+226a=0
a = -1736; b = 226; c = 0;
Δ = b2-4ac
Δ = 2262-4·(-1736)·0
Δ = 51076
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{51076}=226$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(226)-226}{2*-1736}=\frac{-452}{-3472} =113/868 $
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(226)+226}{2*-1736}=\frac{0}{-3472} =0 $

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