(2x*x-8x+6)=(x*x+x-2)

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Solution for (2x*x-8x+6)=(x*x+x-2) equation:



(2x*x-8x+6)=(x*x+x-2)
We move all terms to the left:
(2x*x-8x+6)-((x*x+x-2))=0
We add all the numbers together, and all the variables
(-8x+2x*x+6)-((x+x*x-2))=0
We get rid of parentheses
-8x+2x*x-((x+x*x-2))+6=0
We calculate terms in parentheses: -((x+x*x-2)), so:
(x+x*x-2)
We get rid of parentheses
x+x*x-2
Wy multiply elements
x^2+x-2
Back to the equation:
-(x^2+x-2)
Wy multiply elements
2x^2-8x-(x^2+x-2)+6=0
We get rid of parentheses
2x^2-x^2-8x-x+2+6=0
We add all the numbers together, and all the variables
x^2-9x+8=0
a = 1; b = -9; c = +8;
Δ = b2-4ac
Δ = -92-4·1·8
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-7}{2*1}=\frac{2}{2} =1 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+7}{2*1}=\frac{16}{2} =8 $

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