-5x+x^2/2=12

Solution for -5x+x^2/2=12 equation:

-5x+x^2/2=12

We move all terms to the left:

-5x+x^2/2-(12)=0

We multiply all the terms by the denominator


x^2-5x*2-12*2=0

We add all the numbers together, and all the variables

x^2-5x*2-24=0

Wy multiply elements

x^2-10x-24=0

a = 1; b = -10; c = -24;
Δ = b2-4ac
Δ = -102-4·1·(-24)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-14}{2*1}=\frac{-4}{2}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+14}{2*1}=\frac{24}{2}
=12
$