9r^2+18r=61

Solution for 9r^2+18r=61 equation:

9r^2+18r=61

We move all terms to the left:

9r^2+18r-(61)=0

a = 9; b = 18; c = -61;
Δ = b2-4ac
Δ = 182-4·9·(-61)
Δ = 2520
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:

$\sqrt{\Delta}=\sqrt{2520}=\sqrt{36*70}=\sqrt{36}*\sqrt{70}=6\sqrt{70}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6\sqrt{70}}{2*9}=\frac{-18-6\sqrt{70}}{18}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{70}}{2*9}=\frac{-18+6\sqrt{70}}{18}
$