-9(-5r+1)r=3

Solution for -9(-5r+1)r=3 equation:

-9(-5r+1)r=3

We move all terms to the left:

-9(-5r+1)r-(3)=0

We multiply parentheses

45r^2-9r-3=0

a = 45; b = -9; c = -3;
Δ = b2-4ac
Δ = -92-4·45·(-3)
Δ = 621
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:

$\sqrt{\Delta}=\sqrt{621}=\sqrt{9*69}=\sqrt{9}*\sqrt{69}=3\sqrt{69}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{69}}{2*45}=\frac{9-3\sqrt{69}}{90}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{69}}{2*45}=\frac{9+3\sqrt{69}}{90}
$