4/5k-3=3/10k+7

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Solution for 4/5k-3=3/10k+7 equation:



4/5k-3=3/10k+7
We move all terms to the left:
4/5k-3-(3/10k+7)=0
Domain of the equation: 5k!=0
k!=0/5
k!=0
k∈R
Domain of the equation: 10k+7)!=0
k∈R
We get rid of parentheses
4/5k-3/10k-7-3=0
We calculate fractions
40k/50k^2+(-15k)/50k^2-7-3=0
We add all the numbers together, and all the variables
40k/50k^2+(-15k)/50k^2-10=0
We multiply all the terms by the denominator
40k+(-15k)-10*50k^2=0
Wy multiply elements
-500k^2+40k+(-15k)=0
We get rid of parentheses
-500k^2+40k-15k=0
We add all the numbers together, and all the variables
-500k^2+25k=0
a = -500; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·(-500)·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*-500}=\frac{-50}{-1000} =1/20 $
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*-500}=\frac{0}{-1000} =0 $

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