(41/4)x=71/2

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Solution for (41/4)x=71/2 equation:



(41/4)x=71/2
We move all terms to the left:
(41/4)x-(71/2)=0
Domain of the equation: 4)x!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
(+41/4)x-(+71/2)=0
We multiply parentheses
41x^2-(+71/2)=0
We get rid of parentheses
41x^2-71/2=0
We multiply all the terms by the denominator
41x^2*2-71=0
Wy multiply elements
82x^2-71=0
a = 82; b = 0; c = -71;
Δ = b2-4ac
Δ = 02-4·82·(-71)
Δ = 23288
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{23288}=\sqrt{4*5822}=\sqrt{4}*\sqrt{5822}=2\sqrt{5822}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{5822}}{2*82}=\frac{0-2\sqrt{5822}}{164} =-\frac{2\sqrt{5822}}{164} =-\frac{\sqrt{5822}}{82} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{5822}}{2*82}=\frac{0+2\sqrt{5822}}{164} =\frac{2\sqrt{5822}}{164} =\frac{\sqrt{5822}}{82} $

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