6f(-f+50)=115

Solution for 6f(-f+50)=115 equation:

6f(-f+50)=115

We move all terms to the left:

6f(-f+50)-(115)=0

We add all the numbers together, and all the variables

6f(-1f+50)-115=0

We multiply parentheses

-6f^2+300f-115=0

a = -6; b = 300; c = -115;
Δ = b2-4ac
Δ = 3002-4·(-6)·(-115)
Δ = 87240
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:

$\sqrt{\Delta}=\sqrt{87240}=\sqrt{4*21810}=\sqrt{4}*\sqrt{21810}=2\sqrt{21810}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(300)-2\sqrt{21810}}{2*-6}=\frac{-300-2\sqrt{21810}}{-12}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(300)+2\sqrt{21810}}{2*-6}=\frac{-300+2\sqrt{21810}}{-12}
$