x-119/x+7=-5

Solution for x-119/x+7=-5 equation:

x-119/x+7=-5

We move all terms to the left:

x-119/x+7-(-5)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x-119/x+12=0

We multiply all the terms by the denominator


x*x+12*x-119=0

We add all the numbers together, and all the variables

12x+x*x-119=0

Wy multiply elements

x^2+12x-119=0

a = 1; b = 12; c = -119;
Δ = b2-4ac
Δ = 122-4·1·(-119)
Δ = 620
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:

$\sqrt{\Delta}=\sqrt{620}=\sqrt{4*155}=\sqrt{4}*\sqrt{155}=2\sqrt{155}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{155}}{2*1}=\frac{-12-2\sqrt{155}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{155}}{2*1}=\frac{-12+2\sqrt{155}}{2}
$