6x^2+42x-12=0

Solution for 6x^2+42x-12=0 equation:

6x^2+42x-12=0

a = 6; b = 42; c = -12;
Δ = b2-4ac
Δ = 422-4·6·(-12)
Δ = 2052
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:

$\sqrt{\Delta}=\sqrt{2052}=\sqrt{36*57}=\sqrt{36}*\sqrt{57}=6\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-6\sqrt{57}}{2*6}=\frac{-42-6\sqrt{57}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+6\sqrt{57}}{2*6}=\frac{-42+6\sqrt{57}}{12}
$