(x*x+5x-6)/x-1=0

Solution for (x*x+5x-6)/x-1=0 equation:

(x*x+5x-6)/x-1=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

(5x+x*x-6)/x-1=0

We multiply all the terms by the denominator


(5x+x*x-6)-1*x=0

We add all the numbers together, and all the variables

-1x+(5x+x*x-6)=0

We get rid of parentheses

-1x+5x+x*x-6=0

We add all the numbers together, and all the variables

4x+x*x-6=0

Wy multiply elements

x^2+4x-6=0

a = 1; b = 4; c = -6;
Δ = b2-4ac
Δ = 42-4·1·(-6)
Δ = 40
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{10}}{2*1}=\frac{-4-2\sqrt{10}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{10}}{2*1}=\frac{-4+2\sqrt{10}}{2}
$