6+8f(f=4)

Solution for 6+8f(f=4) equation:

6+8f(f=4)

We move all terms to the left:

6+8f(f-(4))=0

We multiply parentheses

8f^2-32f+6=0

a = 8; b = -32; c = +6;
Δ = b2-4ac
Δ = -322-4·8·6
Δ = 832
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:

$\sqrt{\Delta}=\sqrt{832}=\sqrt{64*13}=\sqrt{64}*\sqrt{13}=8\sqrt{13}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-8\sqrt{13}}{2*8}=\frac{32-8\sqrt{13}}{16}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+8\sqrt{13}}{2*8}=\frac{32+8\sqrt{13}}{16}
$