6+8f(f=4)

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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} $

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