4(x^2+100x-2400)=0

Solution for 4(x^2+100x-2400)=0 equation:

4(x^2+100x-2400)=0

We multiply parentheses

4x^2+400x-9600=0

a = 4; b = 400; c = -9600;
Δ = b2-4ac
Δ = 4002-4·4·(-9600)
Δ = 313600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{313600}=560$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(400)-560}{2*4}=\frac{-960}{8}
=-120
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(400)+560}{2*4}=\frac{160}{8}
=20
$