2r^2-11r^-1+5=0

Solution for 2r^2-11r^-1+5=0 equation:

2r^2-11r^-1+5=0

We add all the numbers together, and all the variables

2r^2-11r+4=0

a = 2; b = -11; c = +4;
Δ = b2-4ac
Δ = -112-4·2·4
Δ = 89
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{89}}{2*2}=\frac{11-\sqrt{89}}{4}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{89}}{2*2}=\frac{11+\sqrt{89}}{4}
$