24x+x^2=54

Solution for 24x+x^2=54 equation:

24x+x^2=54

We move all terms to the left:

24x+x^2-(54)=0

a = 1; b = 24; c = -54;
Δ = b2-4ac
Δ = 242-4·1·(-54)
Δ = 792
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:

$\sqrt{\Delta}=\sqrt{792}=\sqrt{36*22}=\sqrt{36}*\sqrt{22}=6\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-6\sqrt{22}}{2*1}=\frac{-24-6\sqrt{22}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+6\sqrt{22}}{2*1}=\frac{-24+6\sqrt{22}}{2}
$