6x^2-72x-42=0

Solution for 6x^2-72x-42=0 equation:

6x^2-72x-42=0

a = 6; b = -72; c = -42;
Δ = b2-4ac
Δ = -722-4·6·(-42)
Δ = 6192
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:

$\sqrt{\Delta}=\sqrt{6192}=\sqrt{144*43}=\sqrt{144}*\sqrt{43}=12\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-12\sqrt{43}}{2*6}=\frac{72-12\sqrt{43}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+12\sqrt{43}}{2*6}=\frac{72+12\sqrt{43}}{12}
$