-4x+3=5x-13/x

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Solution for -4x+3=5x-13/x equation:



-4x+3=5x-13/x
We move all terms to the left:
-4x+3-(5x-13/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
-4x-(+5x-13/x)+3=0
We get rid of parentheses
-4x-5x+13/x+3=0
We multiply all the terms by the denominator
-4x*x-5x*x+3*x+13=0
We add all the numbers together, and all the variables
3x-4x*x-5x*x+13=0
Wy multiply elements
-4x^2-5x^2+3x+13=0
We add all the numbers together, and all the variables
-9x^2+3x+13=0
a = -9; b = 3; c = +13;
Δ = b2-4ac
Δ = 32-4·(-9)·13
Δ = 477
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:
$\sqrt{\Delta}=\sqrt{477}=\sqrt{9*53}=\sqrt{9}*\sqrt{53}=3\sqrt{53}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{53}}{2*-9}=\frac{-3-3\sqrt{53}}{-18} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{53}}{2*-9}=\frac{-3+3\sqrt{53}}{-18} $

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