-0.5x^2+2x+4=3x-8

Solution for -0.5x^2+2x+4=3x-8 equation:

-0.5x^2+2x+4=3x-8

We move all terms to the left:

-0.5x^2+2x+4-(3x-8)=0

We get rid of parentheses

-0.5x^2+2x-3x+8+4=0

We add all the numbers together, and all the variables

-0.5x^2-1x+12=0

a = -0.5; b = -1; c = +12;
Δ = b2-4ac
Δ = -12-4·(-0.5)·12
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-5}{2*-0.5}=\frac{-4}{-1}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+5}{2*-0.5}=\frac{6}{-1}
=-6
$