x^2+3x-9=x-1+3

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Solution for x^2+3x-9=x-1+3 equation:



x^2+3x-9=x-1+3
We move all terms to the left:
x^2+3x-9-(x-1+3)=0
We add all the numbers together, and all the variables
x^2+3x-(x+2)-9=0
We get rid of parentheses
x^2+3x-x-2-9=0
We add all the numbers together, and all the variables
x^2+2x-11=0
a = 1; b = 2; c = -11;
Δ = b2-4ac
Δ = 22-4·1·(-11)
Δ = 48
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-4\sqrt{3}}{2*1}=\frac{-2-4\sqrt{3}}{2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+4\sqrt{3}}{2*1}=\frac{-2+4\sqrt{3}}{2} $

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