(x+2)(35/x-3)=18

Solution for (x+2)(35/x-3)=18 equation:

(x+2)(35/x-3)=18

We move all terms to the left:

(x+2)(35/x-3)-(18)=0


Domain of the equation: x-3)!=0

x∈R


We multiply parentheses ..

(+35x^2-3x+70x-6)-18=0

We get rid of parentheses

35x^2-3x+70x-6-18=0

We add all the numbers together, and all the variables

35x^2+67x-24=0

a = 35; b = 67; c = -24;
Δ = b2-4ac
Δ = 672-4·35·(-24)
Δ = 7849
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{-(67)-\sqrt{7849}}{2*35}=\frac{-67-\sqrt{7849}}{70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(67)+\sqrt{7849}}{2*35}=\frac{-67+\sqrt{7849}}{70}
$