2x(x-3)=4-x

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Solution for 2x(x-3)=4-x equation:



2x(x-3)=4-x
We move all terms to the left:
2x(x-3)-(4-x)=0
We add all the numbers together, and all the variables
2x(x-3)-(-1x+4)=0
We multiply parentheses
2x^2-6x-(-1x+4)=0
We get rid of parentheses
2x^2-6x+1x-4=0
We add all the numbers together, and all the variables
2x^2-5x-4=0
a = 2; b = -5; c = -4;
Δ = b2-4ac
Δ = -52-4·2·(-4)
Δ = 57
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{-(-5)-\sqrt{57}}{2*2}=\frac{5-\sqrt{57}}{4} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{57}}{2*2}=\frac{5+\sqrt{57}}{4} $

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