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4.5x^2+1-1984=0
We add all the numbers together, and all the variables
4.5x^2-1983=0
a = 4.5; b = 0; c = -1983;
Δ = b2-4ac
Δ = 02-4·4.5·(-1983)
Δ = 35694
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{35694}=\sqrt{9*3966}=\sqrt{9}*\sqrt{3966}=3\sqrt{3966}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-3\sqrt{3966}}{2*4.5}=\frac{0-3\sqrt{3966}}{9} =-\frac{3\sqrt{3966}}{9} =-\frac{\sqrt{3966}}{3} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+3\sqrt{3966}}{2*4.5}=\frac{0+3\sqrt{3966}}{9} =\frac{3\sqrt{3966}}{9} =\frac{\sqrt{3966}}{3} $
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