0=-0.5x^2+0.57x+1.5

Solution for 0=-0.5x^2+0.57x+1.5 equation:

0=-0.5x^2+0.57x+1.5

We move all terms to the left:

0-(-0.5x^2+0.57x+1.5)=0

We add all the numbers together, and all the variables

-(-0.5x^2+0.57x+1.5)=0

We get rid of parentheses

0.5x^2-0.57x-1.5=0

a = 0.5; b = -0.57; c = -1.5;
Δ = b2-4ac
Δ = -0.572-4·0.5·(-1.5)
Δ = 3.3249
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{-(-0.57)-\sqrt{3.3249}}{2*0.5}=\frac{0.57-\sqrt{3.3249}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.57)+\sqrt{3.3249}}{2*0.5}=\frac{0.57+\sqrt{3.3249}}{1}
$