X-5/r=-7

Solution for X-5/r=-7 equation:

X-5/X=-7

We move all terms to the left:

X-5/X-(-7)=0


Domain of the equation: X!=0

X∈R


We add all the numbers together, and all the variables

X-5/X+7=0

We multiply all the terms by the denominator


X*X+7*X-5=0

We add all the numbers together, and all the variables

7X+X*X-5=0

Wy multiply elements

X^2+7X-5=0

a = 1; b = 7; c = -5;
Δ = b2-4ac
Δ = 72-4·1·(-5)
Δ = 69
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{-(7)-\sqrt{69}}{2*1}=\frac{-7-\sqrt{69}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{69}}{2*1}=\frac{-7+\sqrt{69}}{2}
$