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

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



-5/3u+2/5=-7/5u-7
We move all terms to the left:
-5/3u+2/5-(-7/5u-7)=0
Domain of the equation: 3u!=0
u!=0/3
u!=0
u∈R
Domain of the equation: 5u-7)!=0
u∈R
We get rid of parentheses
-5/3u+7/5u+7+2/5=0
We calculate fractions
(-625u)/375u^2+21u/375u^2+6u/375u^2+7=0
We multiply all the terms by the denominator
(-625u)+21u+6u+7*375u^2=0
We add all the numbers together, and all the variables
27u+(-625u)+7*375u^2=0
Wy multiply elements
2625u^2+27u+(-625u)=0
We get rid of parentheses
2625u^2+27u-625u=0
We add all the numbers together, and all the variables
2625u^2-598u=0
a = 2625; b = -598; c = 0;
Δ = b2-4ac
Δ = -5982-4·2625·0
Δ = 357604
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{357604}=598$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-598)-598}{2*2625}=\frac{0}{5250} =0 $
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-598)+598}{2*2625}=\frac{1196}{5250} =598/2625 $

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