3a2-24a-53=0

Solution for 3a2-24a-53=0 equation:

3a^2-24a-53=0

a = 3; b = -24; c = -53;
Δ = b2-4ac
Δ = -242-4·3·(-53)
Δ = 1212
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:

$\sqrt{\Delta}=\sqrt{1212}=\sqrt{4*303}=\sqrt{4}*\sqrt{303}=2\sqrt{303}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{303}}{2*3}=\frac{24-2\sqrt{303}}{6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{303}}{2*3}=\frac{24+2\sqrt{303}}{6}
$