3f-12+15=2/3f+10

Solution for 3f-12+15=2/3f+10 equation:

3f-12+15=2/3f+10

We move all terms to the left:

3f-12+15-(2/3f+10)=0


Domain of the equation: 3f+10)!=0

f∈R


We add all the numbers together, and all the variables

3f-(2/3f+10)+3=0

We get rid of parentheses

3f-2/3f-10+3=0

We multiply all the terms by the denominator


3f*3f-10*3f+3*3f-2=0

Wy multiply elements

9f^2-30f+9f-2=0

We add all the numbers together, and all the variables

9f^2-21f-2=0

a = 9; b = -21; c = -2;
Δ = b2-4ac
Δ = -212-4·9·(-2)
Δ = 513
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:

$\sqrt{\Delta}=\sqrt{513}=\sqrt{9*57}=\sqrt{9}*\sqrt{57}=3\sqrt{57}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3\sqrt{57}}{2*9}=\frac{21-3\sqrt{57}}{18}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3\sqrt{57}}{2*9}=\frac{21+3\sqrt{57}}{18}
$