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10x^2=2
We move all terms to the left:
10x^2-(2)=0
a = 10; b = 0; c = -2;
Δ = b2-4ac
Δ = 02-4·10·(-2)
Δ = 80
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{5}}{2*10}=\frac{0-4\sqrt{5}}{20} =-\frac{4\sqrt{5}}{20} =-\frac{\sqrt{5}}{5} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{5}}{2*10}=\frac{0+4\sqrt{5}}{20} =\frac{4\sqrt{5}}{20} =\frac{\sqrt{5}}{5} $
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