1=7w-10w^2=0

Solution for 1=7w-10w^2=0 equation:

1=7w-10w^2=0

We move all terms to the left:

1-(7w-10w^2)=0

We get rid of parentheses

10w^2-7w+1=0

a = 10; b = -7; c = +1;
Δ = b2-4ac
Δ = -72-4·10·1
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-3}{2*10}=\frac{4}{20}
=1/5
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+3}{2*10}=\frac{10}{20}
=1/2
$