(3x^2-38x-8)=0

Solution for (3x^2-38x-8)=0 equation:

(3x^2-38x-8)=0

We get rid of parentheses

3x^2-38x-8=0

a = 3; b = -38; c = -8;
Δ = b2-4ac
Δ = -382-4·3·(-8)
Δ = 1540
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1540}=\sqrt{4*385}=\sqrt{4}*\sqrt{385}=2\sqrt{385}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-2\sqrt{385}}{2*3}=\frac{38-2\sqrt{385}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+2\sqrt{385}}{2*3}=\frac{38+2\sqrt{385}}{6}
$