(4x^2-3x-144=0)

Solution for (4x^2-3x-144=0) equation:

(4x^2-3x-144=0)

We move all terms to the left:

(4x^2-3x-144-(0))=0

We get rid of parentheses

4x^2-3x-144-0=0

We add all the numbers together, and all the variables

4x^2-3x-144=0

a = 4; b = -3; c = -144;
Δ = b2-4ac
Δ = -32-4·4·(-144)
Δ = 2313
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:

$\sqrt{\Delta}=\sqrt{2313}=\sqrt{9*257}=\sqrt{9}*\sqrt{257}=3\sqrt{257}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{257}}{2*4}=\frac{3-3\sqrt{257}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{257}}{2*4}=\frac{3+3\sqrt{257}}{8}
$