0.25+x(1-x)=10.5*(0.5-x)

Solution for 0.25+x(1-x)=10.5*(0.5-x) equation:

0.25+x(1-x)=10.5*(0.5-x)

We move all terms to the left:

0.25+x(1-x)-(10.5*(0.5-x))=0

We add all the numbers together, and all the variables

x(-1x+1)-(10.5*(-1x+0.5))+0.25=0

We multiply parentheses

-1x^2+x-(10.5*(-1x+0.5))+0.25=0


We calculate terms in parentheses: -(10.5*(-1x+0.5)), so:

10.5*(-1x+0.5)

We multiply parentheses

-10.5x+5.25

Back to the equation:

-(-10.5x+5.25)


We get rid of parentheses

-1x^2+x+10.5x-5.25+0.25=0

We add all the numbers together, and all the variables

-1x^2+11.5x-5=0

a = -1; b = 11.5; c = -5;
Δ = b2-4ac
Δ = 11.52-4·(-1)·(-5)
Δ = 112.25
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{-(11.5)-\sqrt{112.25}}{2*-1}=\frac{-11.5-\sqrt{112.25}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11.5)+\sqrt{112.25}}{2*-1}=\frac{-11.5+\sqrt{112.25}}{-2}
$