4a^2=12a+45

Solution for 4a^2=12a+45 equation:

4a^2=12a+45

We move all terms to the left:

4a^2-(12a+45)=0

We get rid of parentheses

4a^2-12a-45=0

a = 4; b = -12; c = -45;
Δ = b2-4ac
Δ = -122-4·4·(-45)
Δ = 864
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:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{6}}{2*4}=\frac{12-12\sqrt{6}}{8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{6}}{2*4}=\frac{12+12\sqrt{6}}{8}
$