.1w^2+2.155w-180=0

Solution for .1w^2+2.155w-180=0 equation:

.1w^2+2.155w-180=0

a = .1; b = 2.155; c = -180;
Δ = b2-4ac
Δ = 2.1552-4·.1·(-180)
Δ = 76.644025
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{-(2.155)-\sqrt{76.644025}}{2*.1}=\frac{-2.155-\sqrt{76.644025}}{0.2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2.155)+\sqrt{76.644025}}{2*.1}=\frac{-2.155+\sqrt{76.644025}}{0.2}
$