41/2a+31/4a=217

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
$