15/2x+7/x=1

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Solution for 15/2x+7/x=1 equation:



15/2x+7/x=1
We move all terms to the left:
15/2x+7/x-(1)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: x!=0
x∈R
We calculate fractions
15x/2x^2+14x/2x^2-1=0
We multiply all the terms by the denominator
15x+14x-1*2x^2=0
We add all the numbers together, and all the variables
29x-1*2x^2=0
Wy multiply elements
-2x^2+29x=0
a = -2; b = 29; c = 0;
Δ = b2-4ac
Δ = 292-4·(-2)·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-29}{2*-2}=\frac{-58}{-4} =14+1/2 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+29}{2*-2}=\frac{0}{-4} =0 $

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