w^2-2.4w-78.2=0

Solution for w^2-2.4w-78.2=0 equation:

w^2-2.4w-78.2=0

a = 1; b = -2.4; c = -78.2;
Δ = b2-4ac
Δ = -2.42-4·1·(-78.2)
Δ = 318.56
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2.4)-\sqrt{318.56}}{2*1}=\frac{2.4-\sqrt{318.56}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2.4)+\sqrt{318.56}}{2*1}=\frac{2.4+\sqrt{318.56}}{2}
$