(x+40)/(x-5)=X

Solution for (x+40)/(x-5)=X equation:

(x+40)/(x-5)=x

We move all terms to the left:

(x+40)/(x-5)-(x)=0


Domain of the equation: (x-5)!=0

We move all terms containing x to the left, all other terms to the right

x!=5

x∈R


We add all the numbers together, and all the variables

-1x+(x+40)/(x-5)=0

We multiply all the terms by the denominator


-1x*(x-5)+(x+40)=0

We multiply parentheses

-x^2+5x+(x+40)=0

We get rid of parentheses

-x^2+5x+x+40=0

We add all the numbers together, and all the variables

-1x^2+6x+40=0

a = -1; b = 6; c = +40;
Δ = b2-4ac
Δ = 62-4·(-1)·40
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-14}{2*-1}=\frac{-20}{-2}
=+10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+14}{2*-1}=\frac{8}{-2}
=-4
$