(x-2)(x+4)/x+10=0

Solution for (x-2)(x+4)/x+10=0 equation:

(x-2)(x+4)/x+10=0


Domain of the equation: x!=0

x∈R


We multiply parentheses ..

(+x^2+4x-2x-8)/x+10=0

We multiply all the terms by the denominator


(+x^2+4x-2x-8)+10*x=0

We add all the numbers together, and all the variables

(+x^2+4x-2x-8)+10x=0

We get rid of parentheses

x^2+4x-2x+10x-8=0

We add all the numbers together, and all the variables

x^2+12x-8=0

a = 1; b = 12; c = -8;
Δ = b2-4ac
Δ = 122-4·1·(-8)
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{11}}{2*1}=\frac{-12-4\sqrt{11}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{11}}{2*1}=\frac{-12+4\sqrt{11}}{2}
$