9x^2-232x=983^2

Solution for 9x^2-232x=983^2 equation:

9x^2-232x=983^2

We move all terms to the left:

9x^2-232x-(983^2)=0

We add all the numbers together, and all the variables

9x^2-232x-966289=0

a = 9; b = -232; c = -966289;
Δ = b2-4ac
Δ = -2322-4·9·(-966289)
Δ = 34840228
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:

$\sqrt{\Delta}=\sqrt{34840228}=\sqrt{4*8710057}=\sqrt{4}*\sqrt{8710057}=2\sqrt{8710057}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-232)-2\sqrt{8710057}}{2*9}=\frac{232-2\sqrt{8710057}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-232)+2\sqrt{8710057}}{2*9}=\frac{232+2\sqrt{8710057}}{18}
$