1.5x^2+3x=498.5

Solution for 1.5x^2+3x=498.5 equation:

1.5x^2+3x=498.5

We move all terms to the left:

1.5x^2+3x-(498.5)=0

We add all the numbers together, and all the variables

1.5x^2+3x-498.5=0

a = 1.5; b = 3; c = -498.5;
Δ = b2-4ac
Δ = 32-4·1.5·(-498.5)
Δ = 3000
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:

$\sqrt{\Delta}=\sqrt{3000}=\sqrt{100*30}=\sqrt{100}*\sqrt{30}=10\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-10\sqrt{30}}{2*1.5}=\frac{-3-10\sqrt{30}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+10\sqrt{30}}{2*1.5}=\frac{-3+10\sqrt{30}}{3}
$