(9r-5)(2r-9)=0

Solution for (9r-5)(2r-9)=0 equation:

(9r-5)(2r-9)=0

We multiply parentheses ..

(+18r^2-81r-10r+45)=0

We get rid of parentheses

18r^2-81r-10r+45=0

We add all the numbers together, and all the variables

18r^2-91r+45=0

a = 18; b = -91; c = +45;
Δ = b2-4ac
Δ = -912-4·18·45
Δ = 5041
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5041}=71$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-91)-71}{2*18}=\frac{20}{36}
=5/9
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-91)+71}{2*18}=\frac{162}{36}
=4+1/2
$