7(-4f+8)f=6

Solution for 7(-4f+8)f=6 equation:

7(-4f+8)f=6

We move all terms to the left:

7(-4f+8)f-(6)=0

We multiply parentheses

-28f^2+56f-6=0

a = -28; b = 56; c = -6;
Δ = b2-4ac
Δ = 562-4·(-28)·(-6)
Δ = 2464
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:

$\sqrt{\Delta}=\sqrt{2464}=\sqrt{16*154}=\sqrt{16}*\sqrt{154}=4\sqrt{154}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-4\sqrt{154}}{2*-28}=\frac{-56-4\sqrt{154}}{-56}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+4\sqrt{154}}{2*-28}=\frac{-56+4\sqrt{154}}{-56}
$