500x-100x^2=576/100

Solution for 500x-100x^2=576/100 equation:

500x-100x^2=576/100

We move all terms to the left:

500x-100x^2-(576/100)=0

We add all the numbers together, and all the variables

-100x^2+500x-(+576/100)=0

We get rid of parentheses

-100x^2+500x-576/100=0

We multiply all the terms by the denominator


-100x^2*100+500x*100-576=0

Wy multiply elements

-10000x^2+50000x-576=0

a = -10000; b = 50000; c = -576;
Δ = b2-4ac
Δ = 500002-4·(-10000)·(-576)
Δ = 2476960000
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:

$\sqrt{\Delta}=\sqrt{2476960000}=\sqrt{160000*15481}=\sqrt{160000}*\sqrt{15481}=400\sqrt{15481}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50000)-400\sqrt{15481}}{2*-10000}=\frac{-50000-400\sqrt{15481}}{-20000}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50000)+400\sqrt{15481}}{2*-10000}=\frac{-50000+400\sqrt{15481}}{-20000}
$