2(a^2+6)=11a

Solution for 2(a^2+6)=11a equation:

2(a^2+6)=11a

We move all terms to the left:

2(a^2+6)-(11a)=0

We add all the numbers together, and all the variables

-11a+2(a^2+6)=0

We multiply parentheses

2a^2-11a+12=0

a = 2; b = -11; c = +12;
Δ = b2-4ac
Δ = -112-4·2·12
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-5}{2*2}=\frac{6}{4}
=1+1/2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+5}{2*2}=\frac{16}{4}
=4
$