303000=0.04*x^2+25*x+175000

Solution for 303000=0.04*x^2+25*x+175000 equation:

303000=0.04x^2+25x+175000

We move all terms to the left:

303000-(0.04x^2+25x+175000)=0

We get rid of parentheses

-0.04x^2-25x-175000+303000=0

We add all the numbers together, and all the variables

-0.04x^2-25x+128000=0

a = -0.04; b = -25; c = +128000;
Δ = b2-4ac
Δ = -252-4·(-0.04)·128000
Δ = 21105
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:

$\sqrt{\Delta}=\sqrt{21105}=\sqrt{9*2345}=\sqrt{9}*\sqrt{2345}=3\sqrt{2345}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-3\sqrt{2345}}{2*-0.04}=\frac{25-3\sqrt{2345}}{-0.08}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+3\sqrt{2345}}{2*-0.04}=\frac{25+3\sqrt{2345}}{-0.08}
$