69f(57+28f)=69

Solution for 69f(57+28f)=69 equation:

69f(57+28f)=69

We move all terms to the left:

69f(57+28f)-(69)=0

We add all the numbers together, and all the variables

69f(28f+57)-69=0

We multiply parentheses

1932f^2+3933f-69=0

a = 1932; b = 3933; c = -69;
Δ = b2-4ac
Δ = 39332-4·1932·(-69)
Δ = 16001721
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:

$\sqrt{\Delta}=\sqrt{16001721}=\sqrt{4761*3361}=\sqrt{4761}*\sqrt{3361}=69\sqrt{3361}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3933)-69\sqrt{3361}}{2*1932}=\frac{-3933-69\sqrt{3361}}{3864}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3933)+69\sqrt{3361}}{2*1932}=\frac{-3933+69\sqrt{3361}}{3864}
$