(1500)(x)(2)=397.50

Solution for (1500)(x)(2)=397.50 equation:

(1500)(x)(2)=397.50

We move all terms to the left:

(1500)(x)(2)-(397.50)=0

We add all the numbers together, and all the variables

1500x2-(397.5)=0

We add all the numbers together, and all the variables

1500x^2-397.5=0

a = 1500; b = 0; c = -397.5;
Δ = b2-4ac
Δ = 02-4·1500·(-397.5)
Δ = 2385000
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:

$\sqrt{\Delta}=\sqrt{2385000}=\sqrt{22500*106}=\sqrt{22500}*\sqrt{106}=150\sqrt{106}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-150\sqrt{106}}{2*1500}=\frac{0-150\sqrt{106}}{3000}
=-\frac{150\sqrt{106}}{3000}
=-\frac{\sqrt{106}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+150\sqrt{106}}{2*1500}=\frac{0+150\sqrt{106}}{3000}
=\frac{150\sqrt{106}}{3000}
=\frac{\sqrt{106}}{20}
$