x^2+48x+2=0

Solution for x^2+48x+2=0 equation:

x^2+48x+2=0

a = 1; b = 48; c = +2;
Δ = b2-4ac
Δ = 482-4·1·2
Δ = 2296
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:

$\sqrt{\Delta}=\sqrt{2296}=\sqrt{4*574}=\sqrt{4}*\sqrt{574}=2\sqrt{574}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-2\sqrt{574}}{2*1}=\frac{-48-2\sqrt{574}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+2\sqrt{574}}{2*1}=\frac{-48+2\sqrt{574}}{2}
$