11r+5=2r^2

Solution for 11r+5=2r^2 equation:

11r+5=2r^2

We move all terms to the left:

11r+5-(2r^2)=0

determiningTheFunctionDomain
-2r^2+11r+5=0

a = -2; b = 11; c = +5;
Δ = b2-4ac
Δ = 112-4·(-2)·5
Δ = 161
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{-(11)-\sqrt{161}}{2*-2}=\frac{-11-\sqrt{161}}{-4}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{161}}{2*-2}=\frac{-11+\sqrt{161}}{-4}
$