20-4x-18/x=-2x+7

Solution for 20-4x-18/x=-2x+7 equation:

20-4x-18/x=-2x+7

We move all terms to the left:

20-4x-18/x-(-2x+7)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

-4x-18/x+2x-7+20=0

We multiply all the terms by the denominator


-4x*x+2x*x-7*x+20*x-18=0

We add all the numbers together, and all the variables

13x-4x*x+2x*x-18=0

Wy multiply elements

-4x^2+2x^2+13x-18=0

We add all the numbers together, and all the variables

-2x^2+13x-18=0

a = -2; b = 13; c = -18;
Δ = b2-4ac
Δ = 132-4·(-2)·(-18)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-5}{2*-2}=\frac{-18}{-4}
=4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+5}{2*-2}=\frac{-8}{-4}
=+2
$