a-1/3a-1,5=2,5

Solution for a-1/3a-1,5=2,5 equation:

a-1/3a-1.5=2.5

We move all terms to the left:

a-1/3a-1.5-(2.5)=0


Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R


We add all the numbers together, and all the variables

a-1/3a-4=0

We multiply all the terms by the denominator


a*3a-4*3a-1=0

Wy multiply elements

3a^2-12a-1=0

a = 3; b = -12; c = -1;
Δ = b2-4ac
Δ = -122-4·3·(-1)
Δ = 156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{39}}{2*3}=\frac{12-2\sqrt{39}}{6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{39}}{2*3}=\frac{12+2\sqrt{39}}{6}
$