r-4/r-1=0

Solution for r-4/r-1=0 equation:

r-4/r-1=0


Domain of the equation: r!=0

r∈R


We multiply all the terms by the denominator


r*r-1*r-4=0

We add all the numbers together, and all the variables

-1r+r*r-4=0

Wy multiply elements

r^2-1r-4=0

a = 1; b = -1; c = -4;
Δ = b2-4ac
Δ = -12-4·1·(-4)
Δ = 17
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{17}}{2*1}=\frac{1-\sqrt{17}}{2}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{17}}{2*1}=\frac{1+\sqrt{17}}{2}
$