6x^2-3x-42=0

Solution for 6x^2-3x-42=0 equation:

6x^2-3x-42=0

a = 6; b = -3; c = -42;
Δ = b2-4ac
Δ = -32-4·6·(-42)
Δ = 1017
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:

$\sqrt{\Delta}=\sqrt{1017}=\sqrt{9*113}=\sqrt{9}*\sqrt{113}=3\sqrt{113}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{113}}{2*6}=\frac{3-3\sqrt{113}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{113}}{2*6}=\frac{3+3\sqrt{113}}{12}
$