15=5/6*f

Solution for 15=5/6*f equation:

15=5/6*f

We move all terms to the left:

15-(5/6*f)=0


Domain of the equation: 6*f)!=0

f!=0/1

f!=0

f∈R


We add all the numbers together, and all the variables

-(+5/6*f)+15=0

We get rid of parentheses

-5/6*f+15=0

We multiply all the terms by the denominator


15*6*f-5=0

Wy multiply elements

90f*f-5=0

Wy multiply elements

90f^2-5=0

a = 90; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·90·(-5)
Δ = 1800
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:

$\sqrt{\Delta}=\sqrt{1800}=\sqrt{900*2}=\sqrt{900}*\sqrt{2}=30\sqrt{2}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{2}}{2*90}=\frac{0-30\sqrt{2}}{180}
=-\frac{30\sqrt{2}}{180}
=-\frac{\sqrt{2}}{6}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{2}}{2*90}=\frac{0+30\sqrt{2}}{180}
=\frac{30\sqrt{2}}{180}
=\frac{\sqrt{2}}{6}
$