0=4x^2-x-2

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

0=4x^2-x-2

We move all terms to the left:

0-(4x^2-x-2)=0

We add all the numbers together, and all the variables

-(4x^2-x-2)=0

We get rid of parentheses

-4x^2+x+2=0

a = -4; b = 1; c = +2;
Δ = b2-4ac
Δ = 12-4·(-4)·2
Δ = 33
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{33}}{2*-4}=\frac{-1-\sqrt{33}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{33}}{2*-4}=\frac{-1+\sqrt{33}}{-8}
$