9r-5/4r-8=6

Solution for 9r-5/4r-8=6 equation:

9r-5/4r-8=6

We move all terms to the left:

9r-5/4r-8-(6)=0


Domain of the equation: 4r!=0

r!=0/4

r!=0

r∈R


We add all the numbers together, and all the variables

9r-5/4r-14=0

We multiply all the terms by the denominator


9r*4r-14*4r-5=0

Wy multiply elements

36r^2-56r-5=0

a = 36; b = -56; c = -5;
Δ = b2-4ac
Δ = -562-4·36·(-5)
Δ = 3856
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3856}=\sqrt{16*241}=\sqrt{16}*\sqrt{241}=4\sqrt{241}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-4\sqrt{241}}{2*36}=\frac{56-4\sqrt{241}}{72}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+4\sqrt{241}}{2*36}=\frac{56+4\sqrt{241}}{72}
$