3000x(1,03)X=4500

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}
$