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3/8x^2=13
We move all terms to the left:
3/8x^2-(13)=0
Domain of the equation: 8x^2!=0We multiply all the terms by the denominator
x^2!=0/8
x^2!=√0
x!=0
x∈R
-13*8x^2+3=0
Wy multiply elements
-104x^2+3=0
a = -104; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-104)·3
Δ = 1248
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1248}=\sqrt{16*78}=\sqrt{16}*\sqrt{78}=4\sqrt{78}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{78}}{2*-104}=\frac{0-4\sqrt{78}}{-208} =-\frac{4\sqrt{78}}{-208} =-\frac{\sqrt{78}}{-52} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{78}}{2*-104}=\frac{0+4\sqrt{78}}{-208} =\frac{4\sqrt{78}}{-208} =\frac{\sqrt{78}}{-52} $
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