x2+24x-377=0

Solution for x2+24x-377=0 equation:

x2+24x-377=0

We add all the numbers together, and all the variables

x^2+24x-377=0

a = 1; b = 24; c = -377;
Δ = b2-4ac
Δ = 242-4·1·(-377)
Δ = 2084
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:

$\sqrt{\Delta}=\sqrt{2084}=\sqrt{4*521}=\sqrt{4}*\sqrt{521}=2\sqrt{521}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{521}}{2*1}=\frac{-24-2\sqrt{521}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{521}}{2*1}=\frac{-24+2\sqrt{521}}{2}
$