-7/2u+5/2=-4/3u-7

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Solution for -7/2u+5/2=-4/3u-7 equation:



-7/2u+5/2=-4/3u-7
We move all terms to the left:
-7/2u+5/2-(-4/3u-7)=0
Domain of the equation: 2u!=0
u!=0/2
u!=0
u∈R
Domain of the equation: 3u-7)!=0
u∈R
We get rid of parentheses
-7/2u+4/3u+7+5/2=0
We calculate fractions
(-21u)/24u^2+32u/24u^2+15u/24u^2+7=0
We multiply all the terms by the denominator
(-21u)+32u+15u+7*24u^2=0
We add all the numbers together, and all the variables
47u+(-21u)+7*24u^2=0
Wy multiply elements
168u^2+47u+(-21u)=0
We get rid of parentheses
168u^2+47u-21u=0
We add all the numbers together, and all the variables
168u^2+26u=0
a = 168; b = 26; c = 0;
Δ = b2-4ac
Δ = 262-4·168·0
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-26}{2*168}=\frac{-52}{336} =-13/84 $
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+26}{2*168}=\frac{0}{336} =0 $

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