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24=2x*x
We move all terms to the left:
24-(2x*x)=0
We add all the numbers together, and all the variables
-(+2x*x)+24=0
We get rid of parentheses
-2x*x+24=0
Wy multiply elements
-2x^2+24=0
a = -2; b = 0; c = +24;
Δ = b2-4ac
Δ = 02-4·(-2)·24
Δ = 192
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{3}}{2*-2}=\frac{0-8\sqrt{3}}{-4} =-\frac{8\sqrt{3}}{-4} =-\frac{2\sqrt{3}}{-1} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{3}}{2*-2}=\frac{0+8\sqrt{3}}{-4} =\frac{8\sqrt{3}}{-4} =\frac{2\sqrt{3}}{-1} $
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