4f(f-6)+5f=30

Solution for 4f(f-6)+5f=30 equation:

4f(f-6)+5f=30

We move all terms to the left:

4f(f-6)+5f-(30)=0

We add all the numbers together, and all the variables

5f+4f(f-6)-30=0

We multiply parentheses

4f^2+5f-24f-30=0

We add all the numbers together, and all the variables

4f^2-19f-30=0

a = 4; b = -19; c = -30;
Δ = b2-4ac
Δ = -192-4·4·(-30)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-29}{2*4}=\frac{-10}{8}
=-1+1/4
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+29}{2*4}=\frac{48}{8}
=6
$