3a^2-24a-45=0

Solution for 3a^2-24a-45=0 equation:

3a^2-24a-45=0

a = 3; b = -24; c = -45;
Δ = b2-4ac
Δ = -242-4·3·(-45)
Δ = 1116
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:

$\sqrt{\Delta}=\sqrt{1116}=\sqrt{36*31}=\sqrt{36}*\sqrt{31}=6\sqrt{31}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-6\sqrt{31}}{2*3}=\frac{24-6\sqrt{31}}{6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+6\sqrt{31}}{2*3}=\frac{24+6\sqrt{31}}{6}
$