3r-5/r-7=6

Solution for 3r-5/r-7=6 equation:

3r-5/r-7=6

We move all terms to the left:

3r-5/r-7-(6)=0


Domain of the equation: r!=0

r∈R


We add all the numbers together, and all the variables

3r-5/r-13=0

We multiply all the terms by the denominator


3r*r-13*r-5=0

We add all the numbers together, and all the variables

-13r+3r*r-5=0

Wy multiply elements

3r^2-13r-5=0

a = 3; b = -13; c = -5;
Δ = b2-4ac
Δ = -132-4·3·(-5)
Δ = 229
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{-(-13)-\sqrt{229}}{2*3}=\frac{13-\sqrt{229}}{6}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{229}}{2*3}=\frac{13+\sqrt{229}}{6}
$