5r=6/6r=7

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

5r=6/6r=7

We move all terms to the left:

5r-(6/6r)=0


Domain of the equation: 6r)!=0

r!=0/1

r!=0

r∈R


We add all the numbers together, and all the variables

5r-(+6/6r)=0

We get rid of parentheses

5r-6/6r=0

We multiply all the terms by the denominator


5r*6r-6=0

Wy multiply elements

30r^2-6=0

a = 30; b = 0; c = -6;
Δ = b2-4ac
Δ = 02-4·30·(-6)
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{5}}{2*30}=\frac{0-12\sqrt{5}}{60}
=-\frac{12\sqrt{5}}{60}
=-\frac{\sqrt{5}}{5}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{5}}{2*30}=\frac{0+12\sqrt{5}}{60}
=\frac{12\sqrt{5}}{60}
=\frac{\sqrt{5}}{5}
$