3(f+8)f=102

Solution for 3(f+8)f=102 equation:

3(f+8)f=102

We move all terms to the left:

3(f+8)f-(102)=0

We multiply parentheses

3f^2+24f-102=0

a = 3; b = 24; c = -102;
Δ = b2-4ac
Δ = 242-4·3·(-102)
Δ = 1800
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:

$\sqrt{\Delta}=\sqrt{1800}=\sqrt{900*2}=\sqrt{900}*\sqrt{2}=30\sqrt{2}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-30\sqrt{2}}{2*3}=\frac{-24-30\sqrt{2}}{6}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+30\sqrt{2}}{2*3}=\frac{-24+30\sqrt{2}}{6}
$