50w^2-15w+1=0

Solution for 50w^2-15w+1=0 equation:

50w^2-15w+1=0

a = 50; b = -15; c = +1;
Δ = b2-4ac
Δ = -152-4·50·1
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-5}{2*50}=\frac{10}{100}
=1/10
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+5}{2*50}=\frac{20}{100}
=1/5
$