37-8f=-7f(f-6)

Solution for 37-8f=-7f(f-6) equation:

37-8f=-7f(f-6)

We move all terms to the left:

37-8f-(-7f(f-6))=0


We calculate terms in parentheses: -(-7f(f-6)), so:

-7f(f-6)

We multiply parentheses

-7f^2+42f

Back to the equation:

-(-7f^2+42f)


We get rid of parentheses

7f^2-42f-8f+37=0

We add all the numbers together, and all the variables

7f^2-50f+37=0

a = 7; b = -50; c = +37;
Δ = b2-4ac
Δ = -502-4·7·37
Δ = 1464
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:

$\sqrt{\Delta}=\sqrt{1464}=\sqrt{4*366}=\sqrt{4}*\sqrt{366}=2\sqrt{366}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{366}}{2*7}=\frac{50-2\sqrt{366}}{14}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{366}}{2*7}=\frac{50+2\sqrt{366}}{14}
$