3a=1/2a+10

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

3a=1/2a+10

We move all terms to the left:

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


Domain of the equation: 2a+10)!=0

a∈R


We get rid of parentheses

3a-1/2a-10=0

We multiply all the terms by the denominator


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

Wy multiply elements

6a^2-20a-1=0

a = 6; b = -20; c = -1;
Δ = b2-4ac
Δ = -202-4·6·(-1)
Δ = 424
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:

$\sqrt{\Delta}=\sqrt{424}=\sqrt{4*106}=\sqrt{4}*\sqrt{106}=2\sqrt{106}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{106}}{2*6}=\frac{20-2\sqrt{106}}{12}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{106}}{2*6}=\frac{20+2\sqrt{106}}{12}
$