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10x^2+7=927
We move all terms to the left:
10x^2+7-(927)=0
We add all the numbers together, and all the variables
10x^2-920=0
a = 10; b = 0; c = -920;
Δ = b2-4ac
Δ = 02-4·10·(-920)
Δ = 36800
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{36800}=\sqrt{1600*23}=\sqrt{1600}*\sqrt{23}=40\sqrt{23}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{23}}{2*10}=\frac{0-40\sqrt{23}}{20} =-\frac{40\sqrt{23}}{20} =-2\sqrt{23} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{23}}{2*10}=\frac{0+40\sqrt{23}}{20} =\frac{40\sqrt{23}}{20} =2\sqrt{23} $
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