3w^2-4w-21=0

Solution for 3w^2-4w-21=0 equation:

3w^2-4w-21=0

a = 3; b = -4; c = -21;
Δ = b2-4ac
Δ = -42-4·3·(-21)
Δ = 268
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:

$\sqrt{\Delta}=\sqrt{268}=\sqrt{4*67}=\sqrt{4}*\sqrt{67}=2\sqrt{67}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{67}}{2*3}=\frac{4-2\sqrt{67}}{6}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{67}}{2*3}=\frac{4+2\sqrt{67}}{6}
$