3a^2-8a-57=0

Solution for 3a^2-8a-57=0 equation:

3a^2-8a-57=0

a = 3; b = -8; c = -57;
Δ = b2-4ac
Δ = -82-4·3·(-57)
Δ = 748
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:

$\sqrt{\Delta}=\sqrt{748}=\sqrt{4*187}=\sqrt{4}*\sqrt{187}=2\sqrt{187}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{187}}{2*3}=\frac{8-2\sqrt{187}}{6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{187}}{2*3}=\frac{8+2\sqrt{187}}{6}
$