7x+6x=15/x

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Solution for 7x+6x=15/x equation:



7x+6x=15/x
We move all terms to the left:
7x+6x-(15/x)=0
Domain of the equation: x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
7x+6x-(+15/x)=0
We add all the numbers together, and all the variables
13x-(+15/x)=0
We get rid of parentheses
13x-15/x=0
We multiply all the terms by the denominator
13x*x-15=0
Wy multiply elements
13x^2-15=0
a = 13; b = 0; c = -15;
Δ = b2-4ac
Δ = 02-4·13·(-15)
Δ = 780
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{780}=\sqrt{4*195}=\sqrt{4}*\sqrt{195}=2\sqrt{195}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{195}}{2*13}=\frac{0-2\sqrt{195}}{26} =-\frac{2\sqrt{195}}{26} =-\frac{\sqrt{195}}{13} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{195}}{2*13}=\frac{0+2\sqrt{195}}{26} =\frac{2\sqrt{195}}{26} =\frac{\sqrt{195}}{13} $

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