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 get rid of parentheses

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

We multiply all the terms by the denominator


4f*2f-15*2f+6*2f-21=0

Wy multiply elements

8f^2-30f+12f-21=0

We add all the numbers together, and all the variables

8f^2-18f-21=0

a = 8; b = -18; c = -21;
Δ = b2-4ac
Δ = -182-4·8·(-21)
Δ = 996
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:

$\sqrt{\Delta}=\sqrt{996}=\sqrt{4*249}=\sqrt{4}*\sqrt{249}=2\sqrt{249}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{249}}{2*8}=\frac{18-2\sqrt{249}}{16}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{249}}{2*8}=\frac{18+2\sqrt{249}}{16}
$