F(x)=(2x+3)(x-2x)

Solution for F(x)=(2x+3)(x-2x) equation:

(F)=(2F+3)(F-2F)

We move all terms to the left:

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

We add all the numbers together, and all the variables

F-((2F+3)(-1F))=0

We multiply parentheses ..

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


We calculate terms in parentheses: -((-2F^2-3F)), so:

(-2F^2-3F)

We get rid of parentheses

-2F^2-3F

Back to the equation:

-(-2F^2-3F)


We get rid of parentheses

2F^2+3F+F=0

We add all the numbers together, and all the variables

2F^2+4F=0

a = 2; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·2·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*2}=\frac{-8}{4}
=-2
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*2}=\frac{0}{4}
=0
$