w^2-9.5w+21=0

Solution for w^2-9.5w+21=0 equation:

w^2-9.5w+21=0

a = 1; b = -9.5; c = +21;
Δ = b2-4ac
Δ = -9.52-4·1·21
Δ = 6.25
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{-(-9.5)-\sqrt{6.25}}{2*1}=\frac{9.5-\sqrt{6.25}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9.5)+\sqrt{6.25}}{2*1}=\frac{9.5+\sqrt{6.25}}{2}
$