2r^2-r-4=0

Solution for 2r^2-r-4=0 equation:

2r^2-r-4=0

We add all the numbers together, and all the variables

2r^2-1r-4=0

a = 2; b = -1; c = -4;
Δ = b2-4ac
Δ = -12-4·2·(-4)
Δ = 33
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{-(-1)-\sqrt{33}}{2*2}=\frac{1-\sqrt{33}}{4}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{33}}{2*2}=\frac{1+\sqrt{33}}{4}
$