F(x)=x2+5x-2

Solution for F(x)=x2+5x-2 equation:

(F)=F2+5F-2

We move all terms to the left:

(F)-(F2+5F-2)=0

We add all the numbers together, and all the variables

-(+F^2+5F-2)+F=0

We get rid of parentheses

-F^2-5F+F+2=0

We add all the numbers together, and all the variables

-1F^2-4F+2=0

a = -1; b = -4; c = +2;
Δ = b2-4ac
Δ = -42-4·(-1)·2
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{-(-4)-2\sqrt{6}}{2*-1}=\frac{4-2\sqrt{6}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{6}}{2*-1}=\frac{4+2\sqrt{6}}{-2}
$