3000x(1,03)X=4500

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Solution for 3000x(1,03)X=4500 equation:



3000x(1.03)x=4500
We move all terms to the left:
3000x(1.03)x-(4500)=0
We multiply parentheses
3090x^2-4500=0
a = 3090; b = 0; c = -4500;
Δ = b2-4ac
Δ = 02-4·3090·(-4500)
Δ = 55620000
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:
$\sqrt{\Delta}=\sqrt{55620000}=\sqrt{90000*618}=\sqrt{90000}*\sqrt{618}=300\sqrt{618}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-300\sqrt{618}}{2*3090}=\frac{0-300\sqrt{618}}{6180} =-\frac{300\sqrt{618}}{6180} =-\frac{5\sqrt{618}}{103} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+300\sqrt{618}}{2*3090}=\frac{0+300\sqrt{618}}{6180} =\frac{300\sqrt{618}}{6180} =\frac{5\sqrt{618}}{103} $

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