/3a+2a+7=12

Solution for /3a+2a+7=12 equation:

/3a+2a+7=12

We move all terms to the left:

/3a+2a+7-(12)=0


Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R


We add all the numbers together, and all the variables

2a+/3a-5=0

We multiply all the terms by the denominator


2a*3a-5*3a+=0

We add all the numbers together, and all the variables

2a*3a-5*3a=0

Wy multiply elements

6a^2-15a=0

a = 6; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·6·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*6}=\frac{0}{12}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*6}=\frac{30}{12}
=2+1/2
$