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

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

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

We move all terms to the left:

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

We multiply parentheses ..

-((+5F^2+2F-25F-10))+F=0


We calculate terms in parentheses: -((+5F^2+2F-25F-10)), so:

(+5F^2+2F-25F-10)

We get rid of parentheses

5F^2+2F-25F-10

We add all the numbers together, and all the variables

5F^2-23F-10

Back to the equation:

-(5F^2-23F-10)


We add all the numbers together, and all the variables

F-(5F^2-23F-10)=0

We get rid of parentheses

-5F^2+F+23F+10=0

We add all the numbers together, and all the variables

-5F^2+24F+10=0

a = -5; b = 24; c = +10;
Δ = b2-4ac
Δ = 242-4·(-5)·10
Δ = 776
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:

$\sqrt{\Delta}=\sqrt{776}=\sqrt{4*194}=\sqrt{4}*\sqrt{194}=2\sqrt{194}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{194}}{2*-5}=\frac{-24-2\sqrt{194}}{-10}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{194}}{2*-5}=\frac{-24+2\sqrt{194}}{-10}
$