x^2+3x+0,5=-0,5x^2-3x+8

Solution for x^2+3x+0,5=-0,5x^2-3x+8 equation:

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

1.5x^2+6x-7.5=0

a = 1.5; b = 6; c = -7.5;
Δ = b2-4ac
Δ = 62-4·1.5·(-7.5)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-9}{2*1.5}=\frac{-15}{3}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+9}{2*1.5}=\frac{3}{3}
=1
$