1/5x+12=1/7x+18

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Solution for 1/5x+12=1/7x+18 equation:



1/5x+12=1/7x+18
We move all terms to the left:
1/5x+12-(1/7x+18)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
Domain of the equation: 7x+18)!=0
x∈R
We get rid of parentheses
1/5x-1/7x-18+12=0
We calculate fractions
7x/35x^2+(-5x)/35x^2-18+12=0
We add all the numbers together, and all the variables
7x/35x^2+(-5x)/35x^2-6=0
We multiply all the terms by the denominator
7x+(-5x)-6*35x^2=0
Wy multiply elements
-210x^2+7x+(-5x)=0
We get rid of parentheses
-210x^2+7x-5x=0
We add all the numbers together, and all the variables
-210x^2+2x=0
a = -210; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-210)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-210}=\frac{-4}{-420} =1/105 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-210}=\frac{0}{-420} =0 $

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