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-7/2x+7/2=1/5x-19

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Solution for -7/2x+7/2=1/5x-19 equation:



-7/2x+7/2=1/5x-19
We move all terms to the left:
-7/2x+7/2-(1/5x-19)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 5x-19)!=0
x∈R
We get rid of parentheses
-7/2x-1/5x+19+7/2=0
We calculate fractions
(-35x)/40x^2+(-8x)/40x^2+35x/40x^2+19=0
We multiply all the terms by the denominator
(-35x)+(-8x)+35x+19*40x^2=0
We add all the numbers together, and all the variables
35x+(-35x)+(-8x)+19*40x^2=0
Wy multiply elements
760x^2+35x+(-35x)+(-8x)=0
We get rid of parentheses
760x^2+35x-35x-8x=0
We add all the numbers together, and all the variables
760x^2-8x=0
a = 760; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·760·0
Δ = 64
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{64}=8
x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*760}=\frac{0}{1520} =0
x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*760}=\frac{16}{1520} =1/95

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