f^2+4f=33

Solution for f^2+4f=33 equation:

f^2+4f=33

We move all terms to the left:

f^2+4f-(33)=0

a = 1; b = 4; c = -33;
Δ = b2-4ac
Δ = 42-4·1·(-33)
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{37}}{2*1}=\frac{-4-2\sqrt{37}}{2}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{37}}{2*1}=\frac{-4+2\sqrt{37}}{2}
$