r(7/9)=6/5

Solution for r(7/9)=6/5 equation:

r(7/9)=6/5

We move all terms to the left:

r(7/9)-(6/5)=0

We add all the numbers together, and all the variables

r(+7/9)-(+6/5)=0

We multiply parentheses

7r^2-(+6/5)=0

We get rid of parentheses

7r^2-6/5=0

We multiply all the terms by the denominator


7r^2*5-6=0

Wy multiply elements

35r^2-6=0

a = 35; b = 0; c = -6;
Δ = b2-4ac
Δ = 02-4·35·(-6)
Δ = 840
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:

$\sqrt{\Delta}=\sqrt{840}=\sqrt{4*210}=\sqrt{4}*\sqrt{210}=2\sqrt{210}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{210}}{2*35}=\frac{0-2\sqrt{210}}{70}
=-\frac{2\sqrt{210}}{70}
=-\frac{\sqrt{210}}{35}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{210}}{2*35}=\frac{0+2\sqrt{210}}{70}
=\frac{2\sqrt{210}}{70}
=\frac{\sqrt{210}}{35}
$