500+102x+1.5x^2=350x+2.5x^2

Solution for 500+102x+1.5x^2=350x+2.5x^2 equation:

500+102x+1.5x^2=350x+2.5x^2

We move all terms to the left:

500+102x+1.5x^2-(350x+2.5x^2)=0

We get rid of parentheses

1.5x^2-2.5x^2-350x+102x+500=0

We add all the numbers together, and all the variables

-1x^2-248x+500=0

a = -1; b = -248; c = +500;
Δ = b2-4ac
Δ = -2482-4·(-1)·500
Δ = 63504
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{63504}=252$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-248)-252}{2*-1}=\frac{-4}{-2}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-248)+252}{2*-1}=\frac{500}{-2}
=-250
$