3a-1/2a=10+a

Solution for 3a-1/2a=10+a equation:

3a-1/2a=10+a

We move all terms to the left:

3a-1/2a-(10+a)=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R


We add all the numbers together, and all the variables

3a-1/2a-(a+10)=0

We get rid of parentheses

3a-1/2a-a-10=0

We multiply all the terms by the denominator


3a*2a-a*2a-10*2a-1=0

Wy multiply elements

6a^2-2a^2-20a-1=0

We add all the numbers together, and all the variables

4a^2-20a-1=0

a = 4; b = -20; c = -1;
Δ = b2-4ac
Δ = -202-4·4·(-1)
Δ = 416
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:

$\sqrt{\Delta}=\sqrt{416}=\sqrt{16*26}=\sqrt{16}*\sqrt{26}=4\sqrt{26}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{26}}{2*4}=\frac{20-4\sqrt{26}}{8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{26}}{2*4}=\frac{20+4\sqrt{26}}{8}
$