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12-(4x^2)=12-
We move all terms to the left:
12-(4x^2)-(12-)=0
We add all the numbers together, and all the variables
-4x^2+12-0=0
We add all the numbers together, and all the variables
-4x^2+12=0
a = -4; b = 0; c = +12;
Δ = b2-4ac
Δ = 02-4·(-4)·12
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*-4}=\frac{0-8\sqrt{3}}{-8} =-\frac{8\sqrt{3}}{-8} =-\frac{\sqrt{3}}{-1} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{3}}{2*-4}=\frac{0+8\sqrt{3}}{-8} =\frac{8\sqrt{3}}{-8} =\frac{\sqrt{3}}{-1} $
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