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-2=-1/4x^2
We move all terms to the left:
-2-(-1/4x^2)=0
Domain of the equation: 4x^2)!=0We get rid of parentheses
x!=0/1
x!=0
x∈R
1/4x^2-2=0
We multiply all the terms by the denominator
-2*4x^2+1=0
Wy multiply elements
-8x^2+1=0
a = -8; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-8)·1
Δ = 32
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{2}}{2*-8}=\frac{0-4\sqrt{2}}{-16} =-\frac{4\sqrt{2}}{-16} =-\frac{\sqrt{2}}{-4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{2}}{2*-8}=\frac{0+4\sqrt{2}}{-16} =\frac{4\sqrt{2}}{-16} =\frac{\sqrt{2}}{-4} $
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