0=-0.5x^2+x+4.62

Solution for 0=-0.5x^2+x+4.62 equation:

0=-0.5x^2+x+4.62

We move all terms to the left:

0-(-0.5x^2+x+4.62)=0

We add all the numbers together, and all the variables

-(-0.5x^2+x+4.62)=0

We get rid of parentheses

0.5x^2-x-4.62=0

We add all the numbers together, and all the variables

0.5x^2-1x-4.62=0

a = 0.5; b = -1; c = -4.62;
Δ = b2-4ac
Δ = -12-4·0.5·(-4.62)
Δ = 10.24
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{10.24}}{2*0.5}=\frac{1-\sqrt{10.24}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{10.24}}{2*0.5}=\frac{1+\sqrt{10.24}}{1}
$