2r^2+5r+3=9

Solution for 2r^2+5r+3=9 equation:

2r^2+5r+3=9

We move all terms to the left:

2r^2+5r+3-(9)=0

We add all the numbers together, and all the variables

2r^2+5r-6=0

a = 2; b = 5; c = -6;
Δ = b2-4ac
Δ = 52-4·2·(-6)
Δ = 73
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{-(5)-\sqrt{73}}{2*2}=\frac{-5-\sqrt{73}}{4}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{73}}{2*2}=\frac{-5+\sqrt{73}}{4}
$