0=2r^2+11r-21

Solution for 0=2r^2+11r-21 equation:

0=2r^2+11r-21

We move all terms to the left:

0-(2r^2+11r-21)=0

We add all the numbers together, and all the variables

-(2r^2+11r-21)=0

We get rid of parentheses

-2r^2-11r+21=0

a = -2; b = -11; c = +21;
Δ = b2-4ac
Δ = -112-4·(-2)·21
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-17}{2*-2}=\frac{-6}{-4}
=1+1/2
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+17}{2*-2}=\frac{28}{-4}
=-7
$