a=X2-13X+36

Solution for a=X2-13X+36 equation:

a=a2-13a+36

We move all terms to the left:

a-(a2-13a+36)=0

We add all the numbers together, and all the variables

-(+a^2-13a+36)+a=0

We get rid of parentheses

-a^2+13a+a-36=0

We add all the numbers together, and all the variables

-1a^2+14a-36=0

a = -1; b = 14; c = -36;
Δ = b2-4ac
Δ = 142-4·(-1)·(-36)
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{-(14)-2\sqrt{13}}{2*-1}=\frac{-14-2\sqrt{13}}{-2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{13}}{2*-1}=\frac{-14+2\sqrt{13}}{-2}
$