1/5s-11/7s=7/15

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Solution for 1/5s-11/7s=7/15 equation:



1/5s-11/7s=7/15
We move all terms to the left:
1/5s-11/7s-(7/15)=0
Domain of the equation: 5s!=0
s!=0/5
s!=0
s∈R
Domain of the equation: 7s!=0
s!=0/7
s!=0
s∈R
We add all the numbers together, and all the variables
1/5s-11/7s-(+7/15)=0
We get rid of parentheses
1/5s-11/7s-7/15=0
We calculate fractions
(-1715s^2)/525s^2+105s/525s^2+(-825s)/525s^2=0
We multiply all the terms by the denominator
(-1715s^2)+105s+(-825s)=0
We get rid of parentheses
-1715s^2+105s-825s=0
We add all the numbers together, and all the variables
-1715s^2-720s=0
a = -1715; b = -720; c = 0;
Δ = b2-4ac
Δ = -7202-4·(-1715)·0
Δ = 518400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{518400}=720$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-720)-720}{2*-1715}=\frac{0}{-3430} =0 $
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-720)+720}{2*-1715}=\frac{1440}{-3430} =-144/343 $

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