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-(7)=0


Domain of the equation: 6r!=0

r!=0/6

r!=0

r∈R


We multiply all the terms by the denominator


5r*6r-7*6r+6=0

Wy multiply elements

30r^2-42r+6=0

a = 30; b = -42; c = +6;
Δ = b2-4ac
Δ = -422-4·30·6
Δ = 1044
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:

$\sqrt{\Delta}=\sqrt{1044}=\sqrt{36*29}=\sqrt{36}*\sqrt{29}=6\sqrt{29}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-6\sqrt{29}}{2*30}=\frac{42-6\sqrt{29}}{60}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+6\sqrt{29}}{2*30}=\frac{42+6\sqrt{29}}{60}
$