(39x^2-500x-2300)/74000=0

Solution for (39x^2-500x-2300)/74000=0 equation:

(39x^2-500x-2300)/74000=0

We multiply all the terms by the denominator


(39x^2-500x-2300)=0

We get rid of parentheses

39x^2-500x-2300=0

a = 39; b = -500; c = -2300;
Δ = b2-4ac
Δ = -5002-4·39·(-2300)
Δ = 608800
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:

$\sqrt{\Delta}=\sqrt{608800}=\sqrt{400*1522}=\sqrt{400}*\sqrt{1522}=20\sqrt{1522}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-500)-20\sqrt{1522}}{2*39}=\frac{500-20\sqrt{1522}}{78}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-500)+20\sqrt{1522}}{2*39}=\frac{500+20\sqrt{1522}}{78}
$