x=0.71(2-3x+x2)

Solution for x=0.71(2-3x+x2) equation:

x=0.71(2-3x+x2)

We move all terms to the left:

x-(0.71(2-3x+x2))=0

We add all the numbers together, and all the variables

-(0.71(-3x+x^2+2))+x=0


We calculate terms in parentheses: -(0.71(-3x+x^2+2)), so:

0.71(-3x+x^2+2)

We multiply parentheses

0.71x^2-2.13x+1.42

Back to the equation:

-(0.71x^2-2.13x+1.42)


We add all the numbers together, and all the variables

x-(0.71x^2-2.13x+1.42)=0

We get rid of parentheses

-0.71x^2+x+2.13x-1.42=0

We add all the numbers together, and all the variables

-0.71x^2+3.13x-1.42=0

a = -0.71; b = 3.13; c = -1.42;
Δ = b2-4ac
Δ = 3.132-4·(-0.71)·(-1.42)
Δ = 5.7641
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{-(3.13)-\sqrt{5.7641}}{2*-0.71}=\frac{-3.13-\sqrt{5.7641}}{-1.42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3.13)+\sqrt{5.7641}}{2*-0.71}=\frac{-3.13+\sqrt{5.7641}}{-1.42}
$