x^2-x*(0.3+0.35)+0.5*0.35^2+0.3-0.5=0

Solution for x^2-x*(0.3+0.35)+0.5*0.35^2+0.3-0.5=0 equation:

x^2-x(0.3+0.35)+0.5*0.35^2+0.3-0.5=0

We add all the numbers together, and all the variables

x^2-x(0.65)+0.3-0.5+0.5*0.35^2=0

We add all the numbers together, and all the variables

x^2-x(0.65)-0.13875=0

We multiply parentheses

x^2-0.65x-0.13875=0

a = 1; b = -0.65; c = -0.13875;
Δ = b2-4ac
Δ = -0.652-4·1·(-0.13875)
Δ = 0.9775
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{-(-0.65)-\sqrt{0.9775}}{2*1}=\frac{0.65-\sqrt{0.9775}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.65)+\sqrt{0.9775}}{2*1}=\frac{0.65+\sqrt{0.9775}}{2}
$