4f=6+21/2f+15

Solution for 4f=6+21/2f+15 equation:

4f=6+21/2f+15

We move all terms to the left:

4f-(6+21/2f+15)=0


Domain of the equation: 2f+15)!=0

f∈R


We add all the numbers together, and all the variables

4f-(21/2f+21)=0

We get rid of parentheses

4f-21/2f-21=0

We multiply all the terms by the denominator


4f*2f-21*2f-21=0

Wy multiply elements

8f^2-42f-21=0

a = 8; b = -42; c = -21;
Δ = b2-4ac
Δ = -422-4·8·(-21)
Δ = 2436
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:

$\sqrt{\Delta}=\sqrt{2436}=\sqrt{4*609}=\sqrt{4}*\sqrt{609}=2\sqrt{609}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{609}}{2*8}=\frac{42-2\sqrt{609}}{16}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{609}}{2*8}=\frac{42+2\sqrt{609}}{16}
$