f(-4)=-2,f(2)=7

Solution for f(-4)=-2,f(2)=7 equation:

f(-4)=-2.f(2)=7

We move all terms to the left:

f(-4)-(-2.f(2))=0

We add all the numbers together, and all the variables

-(-2f^2)+f(-4)=0

We multiply parentheses

-(-2f^2)-4f=0

We get rid of parentheses

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