2r^2=40-11r

Solution for 2r^2=40-11r equation:

2r^2=40-11r

We move all terms to the left:

2r^2-(40-11r)=0

We add all the numbers together, and all the variables

2r^2-(-11r+40)=0

We get rid of parentheses

2r^2+11r-40=0

a = 2; b = 11; c = -40;
Δ = b2-4ac
Δ = 112-4·2·(-40)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-21}{2*2}=\frac{-32}{4}
=-8
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+21}{2*2}=\frac{10}{4}
=2+1/2
$