x2+3=-2x+9

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Solution for x2+3=-2x+9 equation:



x2+3=-2x+9
We move all terms to the left:
x2+3-(-2x+9)=0
We add all the numbers together, and all the variables
x^2-(-2x+9)+3=0
We get rid of parentheses
x^2+2x-9+3=0
We add all the numbers together, and all the variables
x^2+2x-6=0
a = 1; b = 2; c = -6;
Δ = b2-4ac
Δ = 22-4·1·(-6)
Δ = 28
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:
$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{7}}{2*1}=\frac{-2-2\sqrt{7}}{2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{7}}{2*1}=\frac{-2+2\sqrt{7}}{2} $

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