w^2+6w-75=0

Solution for w^2+6w-75=0 equation:

w^2+6w-75=0

a = 1; b = 6; c = -75;
Δ = b2-4ac
Δ = 62-4·1·(-75)
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-4\sqrt{21}}{2*1}=\frac{-6-4\sqrt{21}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+4\sqrt{21}}{2*1}=\frac{-6+4\sqrt{21}}{2}
$