9a^2=36a-13

Solution for 9a^2=36a-13 equation:

9a^2=36a-13

We move all terms to the left:

9a^2-(36a-13)=0

We get rid of parentheses

9a^2-36a+13=0

a = 9; b = -36; c = +13;
Δ = b2-4ac
Δ = -362-4·9·13
Δ = 828
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:

$\sqrt{\Delta}=\sqrt{828}=\sqrt{36*23}=\sqrt{36}*\sqrt{23}=6\sqrt{23}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-6\sqrt{23}}{2*9}=\frac{36-6\sqrt{23}}{18}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+6\sqrt{23}}{2*9}=\frac{36+6\sqrt{23}}{18}
$