4x2+48x+144=400

Solution for 4x2+48x+144=400 equation:

4x^2+48x+144=400

We move all terms to the left:

4x^2+48x+144-(400)=0

We add all the numbers together, and all the variables

4x^2+48x-256=0

a = 4; b = 48; c = -256;
Δ = b2-4ac
Δ = 482-4·4·(-256)
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-80}{2*4}=\frac{-128}{8}
=-16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+80}{2*4}=\frac{32}{8}
=4
$