2/x-5-4x+7/x+4=0

Solution for 2/x-5-4x+7/x+4=0 equation:

2/x-5-4x+7/x+4=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-4x+2/x+7/x-1=0

We multiply all the terms by the denominator


-4x*x-1*x+2+7=0

We add all the numbers together, and all the variables

-1x-4x*x+9=0

Wy multiply elements

-4x^2-1x+9=0

a = -4; b = -1; c = +9;
Δ = b2-4ac
Δ = -12-4·(-4)·9
Δ = 145
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{-(-1)-\sqrt{145}}{2*-4}=\frac{1-\sqrt{145}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{145}}{2*-4}=\frac{1+\sqrt{145}}{-8}
$