3a2-6a-34=0

Solution for 3a2-6a-34=0 equation:

3a^2-6a-34=0

a = 3; b = -6; c = -34;
Δ = b2-4ac
Δ = -62-4·3·(-34)
Δ = 444
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:

$\sqrt{\Delta}=\sqrt{444}=\sqrt{4*111}=\sqrt{4}*\sqrt{111}=2\sqrt{111}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{111}}{2*3}=\frac{6-2\sqrt{111}}{6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{111}}{2*3}=\frac{6+2\sqrt{111}}{6}
$