x=0.84(2-3x+x2)

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Solution for x=0.84(2-3x+x2) equation: 



x=0.84(2-3x+x2)

We move all terms to the left:

x-(0.84(2-3x+x2))=0

We add all the numbers together, and all the variables

-(0.84(-3x+x^2+2))+x=0



We calculate terms in parentheses: -(0.84(-3x+x^2+2)), so:

0.84(-3x+x^2+2)

We multiply parentheses

0.84x^2-2.52x+1.68

Back to the equation:

-(0.84x^2-2.52x+1.68)



We add all the numbers together, and all the variables

x-(0.84x^2-2.52x+1.68)=0

We get rid of parentheses

-0.84x^2+x+2.52x-1.68=0

We add all the numbers together, and all the variables

-0.84x^2+3.52x-1.68=0

a = -0.84; b = 3.52; c = -1.68;
Δ = b2-4ac
Δ = 3.522-4·(-0.84)·(-1.68)
Δ = 6.7456
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{-(3.52)-\sqrt{6.7456}}{2*-0.84}=\frac{-3.52-\sqrt{6.7456}}{-1.68}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3.52)+\sqrt{6.7456}}{2*-0.84}=\frac{-3.52+\sqrt{6.7456}}{-1.68}
$

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