F(x)=5x^2-7xF(x+3)=

Solution for F(x)=5x^2-7xF(x+3)= equation:

(F)=5F^2-7F(F+3)=

We move all terms to the left:

(F)-(5F^2-7F(F+3))=0


We calculate terms in parentheses: -(5F^2-7F(F+3)), so:

5F^2-7F(F+3)

We multiply parentheses

5F^2-7F^2-21F

We add all the numbers together, and all the variables

-2F^2-21F

Back to the equation:

-(-2F^2-21F)


We get rid of parentheses

2F^2+21F+F=0

We add all the numbers together, and all the variables

2F^2+22F=0

a = 2; b = 22; c = 0;
Δ = b2-4ac
Δ = 222-4·2·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-22}{2*2}=\frac{-44}{4}
=-11
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+22}{2*2}=\frac{0}{4}
=0
$