3f^2-48f=-117

Solution for 3f^2-48f=-117 equation:

3f^2-48f=-117

We move all terms to the left:

3f^2-48f-(-117)=0

We add all the numbers together, and all the variables

3f^2-48f+117=0

a = 3; b = -48; c = +117;
Δ = b2-4ac
Δ = -482-4·3·117
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-30}{2*3}=\frac{18}{6}
=3
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+30}{2*3}=\frac{78}{6}
=13
$