2r^2+9r=5

Solution for 2r^2+9r=5 equation:

2r^2+9r=5

We move all terms to the left:

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

a = 2; b = 9; c = -5;
Δ = b2-4ac
Δ = 92-4·2·(-5)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-11}{2*2}=\frac{-20}{4}
=-5
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+11}{2*2}=\frac{2}{4}
=1/2
$