1234x^2+1234x=56789

Solution for 1234x^2+1234x=56789 equation:

1234x^2+1234x=56789

We move all terms to the left:

1234x^2+1234x-(56789)=0

a = 1234; b = 1234; c = -56789;
Δ = b2-4ac
Δ = 12342-4·1234·(-56789)
Δ = 281833260
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:

$\sqrt{\Delta}=\sqrt{281833260}=\sqrt{4*70458315}=\sqrt{4}*\sqrt{70458315}=2\sqrt{70458315}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1234)-2\sqrt{70458315}}{2*1234}=\frac{-1234-2\sqrt{70458315}}{2468}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1234)+2\sqrt{70458315}}{2*1234}=\frac{-1234+2\sqrt{70458315}}{2468}
$