(x^2+6x-55)/x-5=0

Solution for (x^2+6x-55)/x-5=0 equation:

(x^2+6x-55)/x-5=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


(x^2+6x-55)-5*x=0

We add all the numbers together, and all the variables

-5x+(x^2+6x-55)=0

We get rid of parentheses

x^2-5x+6x-55=0

We add all the numbers together, and all the variables

x^2+x-55=0

a = 1; b = 1; c = -55;
Δ = b2-4ac
Δ = 12-4·1·(-55)
Δ = 221
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{221}}{2*1}=\frac{-1-\sqrt{221}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{221}}{2*1}=\frac{-1+\sqrt{221}}{2}
$