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10x^2=6789
We move all terms to the left:
10x^2-(6789)=0
a = 10; b = 0; c = -6789;
Δ = b2-4ac
Δ = 02-4·10·(-6789)
Δ = 271560
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{271560}=\sqrt{4*67890}=\sqrt{4}*\sqrt{67890}=2\sqrt{67890}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{67890}}{2*10}=\frac{0-2\sqrt{67890}}{20} =-\frac{2\sqrt{67890}}{20} =-\frac{\sqrt{67890}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{67890}}{2*10}=\frac{0+2\sqrt{67890}}{20} =\frac{2\sqrt{67890}}{20} =\frac{\sqrt{67890}}{10} $
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