3a^2-6a-45=3

Solution for 3a^2-6a-45=3 equation:

3a^2-6a-45=3

We move all terms to the left:

3a^2-6a-45-(3)=0

We add all the numbers together, and all the variables

3a^2-6a-48=0

a = 3; b = -6; c = -48;
Δ = b2-4ac
Δ = -62-4·3·(-48)
Δ = 612
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:

$\sqrt{\Delta}=\sqrt{612}=\sqrt{36*17}=\sqrt{36}*\sqrt{17}=6\sqrt{17}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{17}}{2*3}=\frac{6-6\sqrt{17}}{6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{17}}{2*3}=\frac{6+6\sqrt{17}}{6}
$