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

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}
$