7w^2-8w-21=0

Solution for 7w^2-8w-21=0 equation:

7w^2-8w-21=0

a = 7; b = -8; c = -21;
Δ = b2-4ac
Δ = -82-4·7·(-21)
Δ = 652
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:

$\sqrt{\Delta}=\sqrt{652}=\sqrt{4*163}=\sqrt{4}*\sqrt{163}=2\sqrt{163}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{163}}{2*7}=\frac{8-2\sqrt{163}}{14}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{163}}{2*7}=\frac{8+2\sqrt{163}}{14}
$