x^2+14x+48=288

Solution for x^2+14x+48=288 equation:

x^2+14x+48=288

We move all terms to the left:

x^2+14x+48-(288)=0

We add all the numbers together, and all the variables

x^2+14x-240=0

a = 1; b = 14; c = -240;
Δ = b2-4ac
Δ = 142-4·1·(-240)
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-34}{2*1}=\frac{-48}{2}
=-24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+34}{2*1}=\frac{20}{2}
=10
$