5r(r+9)-2(1-r)=1

Solution for 5r(r+9)-2(1-r)=1 equation:

5r(r+9)-2(1-r)=1

We move all terms to the left:

5r(r+9)-2(1-r)-(1)=0

We add all the numbers together, and all the variables

5r(r+9)-2(-1r+1)-1=0

We multiply parentheses

5r^2+45r+2r-2-1=0

We add all the numbers together, and all the variables

5r^2+47r-3=0

a = 5; b = 47; c = -3;
Δ = b2-4ac
Δ = 472-4·5·(-3)
Δ = 2269
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(47)-\sqrt{2269}}{2*5}=\frac{-47-\sqrt{2269}}{10}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(47)+\sqrt{2269}}{2*5}=\frac{-47+\sqrt{2269}}{10}
$