F(-3)=-1/2x^2

Solution for F(-3)=-1/2x^2 equation:

(-3)=-1/2F^2

We move all terms to the left:

(-3)-(-1/2F^2)=0


Domain of the equation: 2F^2)!=0

F!=0/1

F!=0

F∈R


We add all the numbers together, and all the variables

-(-1/2F^2)-3=0

We get rid of parentheses

1/2F^2-3=0

We multiply all the terms by the denominator


-3*2F^2+1=0

Wy multiply elements

-6F^2+1=0

a = -6; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-6)·1
Δ = 24
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{6}}{2*-6}=\frac{0-2\sqrt{6}}{-12}
=-\frac{2\sqrt{6}}{-12}
=-\frac{\sqrt{6}}{-6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{6}}{2*-6}=\frac{0+2\sqrt{6}}{-12}
=\frac{2\sqrt{6}}{-12}
=\frac{\sqrt{6}}{-6}
$