6w^2-26w-42=0

Solution for 6w^2-26w-42=0 equation:

6w^2-26w-42=0

a = 6; b = -26; c = -42;
Δ = b2-4ac
Δ = -262-4·6·(-42)
Δ = 1684
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1684}=\sqrt{4*421}=\sqrt{4}*\sqrt{421}=2\sqrt{421}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{421}}{2*6}=\frac{26-2\sqrt{421}}{12}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{421}}{2*6}=\frac{26+2\sqrt{421}}{12}
$