F(x)=x^2-3/4

Solution for F(x)=x^2-3/4 equation:

(F)=F^2-3/4

We move all terms to the left:

(F)-(F^2-3/4)=0

We get rid of parentheses

-F^2+F+3/4=0

We multiply all the terms by the denominator


-F^2*4+F*4+3=0

Wy multiply elements

-4F^2+4F+3=0

a = -4; b = 4; c = +3;
Δ = b2-4ac
Δ = 42-4·(-4)·3
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-8}{2*-4}=\frac{-12}{-8}
=1+1/2
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+8}{2*-4}=\frac{4}{-8}
=-1/2
$