F(x)=x2+3x-40

Solution for F(x)=x2+3x-40 equation:

(F)=F2+3F-40

We move all terms to the left:

(F)-(F2+3F-40)=0

We add all the numbers together, and all the variables

-(+F^2+3F-40)+F=0

We get rid of parentheses

-F^2-3F+F+40=0

We add all the numbers together, and all the variables

-1F^2-2F+40=0

a = -1; b = -2; c = +40;
Δ = b2-4ac
Δ = -22-4·(-1)·40
Δ = 164
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:

$\sqrt{\Delta}=\sqrt{164}=\sqrt{4*41}=\sqrt{4}*\sqrt{41}=2\sqrt{41}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{41}}{2*-1}=\frac{2-2\sqrt{41}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{41}}{2*-1}=\frac{2+2\sqrt{41}}{-2}
$