289x=24+x^2

Solution for 289x=24+x^2 equation:

289x=24+x^2

We move all terms to the left:

289x-(24+x^2)=0

We get rid of parentheses

-x^2+289x-24=0

We add all the numbers together, and all the variables

-1x^2+289x-24=0

a = -1; b = 289; c = -24;
Δ = b2-4ac
Δ = 2892-4·(-1)·(-24)
Δ = 83425
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:

$\sqrt{\Delta}=\sqrt{83425}=\sqrt{25*3337}=\sqrt{25}*\sqrt{3337}=5\sqrt{3337}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(289)-5\sqrt{3337}}{2*-1}=\frac{-289-5\sqrt{3337}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(289)+5\sqrt{3337}}{2*-1}=\frac{-289+5\sqrt{3337}}{-2}
$