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15=x^2+6x+3
We move all terms to the left:
15-(x^2+6x+3)=0
We get rid of parentheses
-x^2-6x-3+15=0
We add all the numbers together, and all the variables
-1x^2-6x+12=0
a = -1; b = -6; c = +12;
Δ = b2-4ac
Δ = -62-4·(-1)·12
Δ = 84
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{21}}{2*-1}=\frac{6-2\sqrt{21}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{21}}{2*-1}=\frac{6+2\sqrt{21}}{-2} $
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