x^2+48x+76=0

Solution for x^2+48x+76=0 equation:

x^2+48x+76=0

a = 1; b = 48; c = +76;
Δ = b2-4ac
Δ = 482-4·1·76
Δ = 2000
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:

$\sqrt{\Delta}=\sqrt{2000}=\sqrt{400*5}=\sqrt{400}*\sqrt{5}=20\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-20\sqrt{5}}{2*1}=\frac{-48-20\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+20\sqrt{5}}{2*1}=\frac{-48+20\sqrt{5}}{2}
$