2r^2+5r=-3

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

2r^2+5r=-3

We move all terms to the left:

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

We add all the numbers together, and all the variables

2r^2+5r+3=0

a = 2; b = 5; c = +3;
Δ = b2-4ac
Δ = 52-4·2·3
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-1}{2*2}=\frac{-6}{4}
=-1+1/2
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+1}{2*2}=\frac{-4}{4}
=-1
$