F(x)=(x+5)(x-2)

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

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

We move all terms to the left:

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

We multiply parentheses ..

-((+F^2-2F+5F-10))+F=0


We calculate terms in parentheses: -((+F^2-2F+5F-10)), so:

(+F^2-2F+5F-10)

We get rid of parentheses

F^2-2F+5F-10

We add all the numbers together, and all the variables

F^2+3F-10

Back to the equation:

-(F^2+3F-10)


We add all the numbers together, and all the variables

F-(F^2+3F-10)=0

We get rid of parentheses

-F^2+F-3F+10=0

We add all the numbers together, and all the variables

-1F^2-2F+10=0

a = -1; b = -2; c = +10;
Δ = b2-4ac
Δ = -22-4·(-1)·10
Δ = 44
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:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{11}}{2*-1}=\frac{2-2\sqrt{11}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{11}}{2*-1}=\frac{2+2\sqrt{11}}{-2}
$