(39x^2-478x-2459)/(77023)=0

Solution for (39x^2-478x-2459)/(77023)=0 equation:

(39x^2-478x-2459)/(77023)=0

We multiply all the terms by the denominator


(39x^2-478x-2459)=0

We get rid of parentheses

39x^2-478x-2459=0

a = 39; b = -478; c = -2459;
Δ = b2-4ac
Δ = -4782-4·39·(-2459)
Δ = 612088
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:

$\sqrt{\Delta}=\sqrt{612088}=\sqrt{4*153022}=\sqrt{4}*\sqrt{153022}=2\sqrt{153022}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-478)-2\sqrt{153022}}{2*39}=\frac{478-2\sqrt{153022}}{78}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-478)+2\sqrt{153022}}{2*39}=\frac{478+2\sqrt{153022}}{78}
$