5+31/2x=6+21/4x

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Solution for 5+31/2x=6+21/4x equation:



5+31/2x=6+21/4x
We move all terms to the left:
5+31/2x-(6+21/4x)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 4x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
31/2x-(21/4x+6)+5=0
We get rid of parentheses
31/2x-21/4x-6+5=0
We calculate fractions
124x/8x^2+(-42x)/8x^2-6+5=0
We add all the numbers together, and all the variables
124x/8x^2+(-42x)/8x^2-1=0
We multiply all the terms by the denominator
124x+(-42x)-1*8x^2=0
Wy multiply elements
-8x^2+124x+(-42x)=0
We get rid of parentheses
-8x^2+124x-42x=0
We add all the numbers together, and all the variables
-8x^2+82x=0
a = -8; b = 82; c = 0;
Δ = b2-4ac
Δ = 822-4·(-8)·0
Δ = 6724
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6724}=82$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(82)-82}{2*-8}=\frac{-164}{-16} =10+1/4 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(82)+82}{2*-8}=\frac{0}{-16} =0 $

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