-77.73w^2+131.75w-2.475=0

Solution for -77.73w^2+131.75w-2.475=0 equation:

-77.73w^2+131.75w-2.475=0

a = -77.73; b = 131.75; c = -2.475;
Δ = b2-4ac
Δ = 131.752-4·(-77.73)·(-2.475)
Δ = 16588.5355
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{-(131.75)-\sqrt{16588.5355}}{2*-77.73}=\frac{-131.75-\sqrt{16588.5355}}{-155.46}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(131.75)+\sqrt{16588.5355}}{2*-77.73}=\frac{-131.75+\sqrt{16588.5355}}{-155.46}
$