F(x)=x2+3x-8

Solution for F(x)=x2+3x-8 equation:

(F)=F2+3F-8

We move all terms to the left:

(F)-(F2+3F-8)=0

We add all the numbers together, and all the variables

-(+F^2+3F-8)+F=0

We get rid of parentheses

-F^2-3F+F+8=0

We add all the numbers together, and all the variables

-1F^2-2F+8=0

a = -1; b = -2; c = +8;
Δ = b2-4ac
Δ = -22-4·(-1)·8
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-6}{2*-1}=\frac{-4}{-2}
=+2
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+6}{2*-1}=\frac{8}{-2}
=-4
$