2a+70/6a=12

Solution for 2a+70/6a=12 equation:

2a+70/6a=12

We move all terms to the left:

2a+70/6a-(12)=0


Domain of the equation: 6a!=0

a!=0/6

a!=0

a∈R


We multiply all the terms by the denominator


2a*6a-12*6a+70=0

Wy multiply elements

12a^2-72a+70=0

a = 12; b = -72; c = +70;
Δ = b2-4ac
Δ = -722-4·12·70
Δ = 1824
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:

$\sqrt{\Delta}=\sqrt{1824}=\sqrt{16*114}=\sqrt{16}*\sqrt{114}=4\sqrt{114}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-4\sqrt{114}}{2*12}=\frac{72-4\sqrt{114}}{24}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+4\sqrt{114}}{2*12}=\frac{72+4\sqrt{114}}{24}
$