A=6+5a+a^2/2

Solution for A=6+5a+a^2/2 equation:

=6+5A+A^2/2

We move all terms to the left:

-(6+5A+A^2/2)=0

We get rid of parentheses

-A^2/2-5A-6=0

We multiply all the terms by the denominator


-A^2-5A*2-6*2=0

We add all the numbers together, and all the variables

-1A^2-5A*2-12=0

Wy multiply elements

-1A^2-10A-12=0

a = -1; b = -10; c = -12;
Δ = b2-4ac
Δ = -102-4·(-1)·(-12)
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{13}}{2*-1}=\frac{10-2\sqrt{13}}{-2}
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{13}}{2*-1}=\frac{10+2\sqrt{13}}{-2}
$