0=-4.867x^2+4.564x+2.083

Solution for 0=-4.867x^2+4.564x+2.083 equation:

0=-4.867x^2+4.564x+2.083

We move all terms to the left:

0-(-4.867x^2+4.564x+2.083)=0

We add all the numbers together, and all the variables

-(-4.867x^2+4.564x+2.083)=0

We get rid of parentheses

4.867x^2-4.564x-2.083=0

a = 4.867; b = -4.564; c = -2.083;
Δ = b2-4ac
Δ = -4.5642-4·4.867·(-2.083)
Δ = 61.38194
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{-(-4.564)-\sqrt{61.38194}}{2*4.867}=\frac{4.564-\sqrt{61.38194}}{9.734}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4.564)+\sqrt{61.38194}}{2*4.867}=\frac{4.564+\sqrt{61.38194}}{9.734}
$