X-7/x=-13

Solution for X-7/x=-13 equation:

X-7/X=-13

We move all terms to the left:

X-7/X-(-13)=0


Domain of the equation: X!=0

X∈R


We add all the numbers together, and all the variables

X-7/X+13=0

We multiply all the terms by the denominator


X*X+13*X-7=0

We add all the numbers together, and all the variables

13X+X*X-7=0

Wy multiply elements

X^2+13X-7=0

a = 1; b = 13; c = -7;
Δ = b2-4ac
Δ = 132-4·1·(-7)
Δ = 197
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{-(13)-\sqrt{197}}{2*1}=\frac{-13-\sqrt{197}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{197}}{2*1}=\frac{-13+\sqrt{197}}{2}
$