0.1=3.5x-3.5x^2

Solution for 0.1=3.5x-3.5x^2 equation:

0.1=3.5x-3.5x^2

We move all terms to the left:

0.1-(3.5x-3.5x^2)=0

We get rid of parentheses

3.5x^2-3.5x+0.1=0

a = 3.5; b = -3.5; c = +0.1;
Δ = b2-4ac
Δ = -3.52-4·3.5·0.1
Δ = 10.85
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3.5)-\sqrt{10.85}}{2*3.5}=\frac{3.5-\sqrt{10.85}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3.5)+\sqrt{10.85}}{2*3.5}=\frac{3.5+\sqrt{10.85}}{7}
$