120x+x2=544

Solution for 120x+x2=544 equation:

120x+x2=544

We move all terms to the left:

120x+x2-(544)=0

We add all the numbers together, and all the variables

x^2+120x-544=0

a = 1; b = 120; c = -544;
Δ = b2-4ac
Δ = 1202-4·1·(-544)
Δ = 16576
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:

$\sqrt{\Delta}=\sqrt{16576}=\sqrt{64*259}=\sqrt{64}*\sqrt{259}=8\sqrt{259}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-8\sqrt{259}}{2*1}=\frac{-120-8\sqrt{259}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+8\sqrt{259}}{2*1}=\frac{-120+8\sqrt{259}}{2}
$