E=3x-21/x

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Solution for E=3x-21/x equation:



=3E-21/E
We move all terms to the left:
-(3E-21/E)=0
Domain of the equation: E)!=0
E!=0/1
E!=0
E∈R
We add all the numbers together, and all the variables
-(+3E-21/E)=0
We get rid of parentheses
-3E+21/E=0
We multiply all the terms by the denominator
-3E*E+21=0
Wy multiply elements
-3E^2+21=0
a = -3; b = 0; c = +21;
Δ = b2-4ac
Δ = 02-4·(-3)·21
Δ = 252
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$E_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$E_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{252}=\sqrt{36*7}=\sqrt{36}*\sqrt{7}=6\sqrt{7}$
$E_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{7}}{2*-3}=\frac{0-6\sqrt{7}}{-6} =-\frac{6\sqrt{7}}{-6} =-\frac{\sqrt{7}}{-1} $
$E_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{7}}{2*-3}=\frac{0+6\sqrt{7}}{-6} =\frac{6\sqrt{7}}{-6} =\frac{\sqrt{7}}{-1} $

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