(-x^2)/2-5x/2+4=0

Solution for (-x^2)/2-5x/2+4=0 equation:

(-x^2)/2-5x/2+4=0

We multiply all the terms by the denominator


(-x^2)-5x+4*2=0

We add all the numbers together, and all the variables

(-x^2)-5x+8=0

We get rid of parentheses

-x^2-5x+8=0

We add all the numbers together, and all the variables

-1x^2-5x+8=0

a = -1; b = -5; c = +8;
Δ = b2-4ac
Δ = -52-4·(-1)·8
Δ = 57
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{-(-5)-\sqrt{57}}{2*-1}=\frac{5-\sqrt{57}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{57}}{2*-1}=\frac{5+\sqrt{57}}{-2}
$