41-8x=-6x-23/x=-9

Solution for 41-8x=-6x-23/x=-9 equation:

41-8x=-6x-23/x=-9

We move all terms to the left:

41-8x-(-6x-23/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

-8x+6x+23/x+41=0

We multiply all the terms by the denominator


-8x*x+6x*x+41*x+23=0

We add all the numbers together, and all the variables

41x-8x*x+6x*x+23=0

Wy multiply elements

-8x^2+6x^2+41x+23=0

We add all the numbers together, and all the variables

-2x^2+41x+23=0

a = -2; b = 41; c = +23;
Δ = b2-4ac
Δ = 412-4·(-2)·23
Δ = 1865
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(41)-\sqrt{1865}}{2*-2}=\frac{-41-\sqrt{1865}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+\sqrt{1865}}{2*-2}=\frac{-41+\sqrt{1865}}{-4}
$