8/9r+5/6r=62

Solution for 8/9r+5/6r=62 equation:

8/9r+5/6r=62

We move all terms to the left:

8/9r+5/6r-(62)=0


Domain of the equation: 9r!=0

r!=0/9

r!=0

r∈R



Domain of the equation: 6r!=0

r!=0/6

r!=0

r∈R


We calculate fractions


48r/54r^2+45r/54r^2-62=0

We multiply all the terms by the denominator


48r+45r-62*54r^2=0

We add all the numbers together, and all the variables

93r-62*54r^2=0

Wy multiply elements

-3348r^2+93r=0

a = -3348; b = 93; c = 0;
Δ = b2-4ac
Δ = 932-4·(-3348)·0
Δ = 8649
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8649}=93$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(93)-93}{2*-3348}=\frac{-186}{-6696}
=1/36
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(93)+93}{2*-3348}=\frac{0}{-6696}
=0
$