.5r(r+2.75)=3

Solution for .5r(r+2.75)=3 equation:

.5r(r+2.75)=3

We move all terms to the left:

.5r(r+2.75)-(3)=0

We multiply parentheses

r^2+2.75r-3=0

a = 1; b = 2.75; c = -3;
Δ = b2-4ac
Δ = 2.752-4·1·(-3)
Δ = 19.5625
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{-(2.75)-\sqrt{19.5625}}{2*1}=\frac{-2.75-\sqrt{19.5625}}{2}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2.75)+\sqrt{19.5625}}{2*1}=\frac{-2.75+\sqrt{19.5625}}{2}
$