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

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

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

We get rid of parentheses

-x^2/2-2x+5=0

We multiply all the terms by the denominator


-x^2-2x*2+5*2=0

We add all the numbers together, and all the variables

-1x^2-2x*2+10=0

Wy multiply elements

-1x^2-4x+10=0

a = -1; b = -4; c = +10;
Δ = b2-4ac
Δ = -42-4·(-1)·10
Δ = 56
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{14}}{2*-1}=\frac{4-2\sqrt{14}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{14}}{2*-1}=\frac{4+2\sqrt{14}}{-2}
$