12x+x^2=589

Solution for 12x+x^2=589 equation:

12x+x^2=589

We move all terms to the left:

12x+x^2-(589)=0

a = 1; b = 12; c = -589;
Δ = b2-4ac
Δ = 122-4·1·(-589)
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-50}{2*1}=\frac{-62}{2}
=-31
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+50}{2*1}=\frac{38}{2}
=19
$