0=-32x^2/2500+x+180

Solution for 0=-32x^2/2500+x+180 equation:

0=-32x^2/2500+x+180

We move all terms to the left:

0-(-32x^2/2500+x+180)=0


Domain of the equation: 2500+x+180)!=0

We move all terms containing x to the left, all other terms to the right

x+180)!=-2500

x∈R


We add all the numbers together, and all the variables

-(-32x^2/2500+x+180)=0

We get rid of parentheses

32x^2/2500-x-180=0

We multiply all the terms by the denominator


32x^2-x*2500-180*2500=0

We add all the numbers together, and all the variables

32x^2-x*2500-450000=0

Wy multiply elements

32x^2-2500x-450000=0

a = 32; b = -2500; c = -450000;
Δ = b2-4ac
Δ = -25002-4·32·(-450000)
Δ = 63850000
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:

$\sqrt{\Delta}=\sqrt{63850000}=\sqrt{10000*6385}=\sqrt{10000}*\sqrt{6385}=100\sqrt{6385}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2500)-100\sqrt{6385}}{2*32}=\frac{2500-100\sqrt{6385}}{64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2500)+100\sqrt{6385}}{2*32}=\frac{2500+100\sqrt{6385}}{64}
$