0=-0,5*(x*x)+5*x-8

Solution for 0=-0,5*(x*x)+5*x-8 equation:

0=-0.5(x*x)+5x-8

We move all terms to the left:

0-(-0.5(x*x)+5x-8)=0

We add all the numbers together, and all the variables

-(-0.5(+x*x)+5x-8)+0=0

We add all the numbers together, and all the variables

-(-0.5(+x*x)+5x-8)=0


We calculate terms in parentheses: -(-0.5(+x*x)+5x-8), so:

-0.5(+x*x)+5x-8

We add all the numbers together, and all the variables

5x-0.5(+x*x)-8

We multiply parentheses

-0.5x^2+5x-8

Back to the equation:

-(-0.5x^2+5x-8)


We get rid of parentheses

0.5x^2-5x+8=0

a = 0.5; b = -5; c = +8;
Δ = b2-4ac
Δ = -52-4·0.5·8
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3}{2*0.5}=\frac{2}{1}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3}{2*0.5}=\frac{8}{1}
=8
$