4x^2-24=144

Solution for 4x^2-24=144 equation:

4x^2-24=144

We move all terms to the left:

4x^2-24-(144)=0

We add all the numbers together, and all the variables

4x^2-168=0

a = 4; b = 0; c = -168;
Δ = b2-4ac
Δ = 02-4·4·(-168)
Δ = 2688
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:

$\sqrt{\Delta}=\sqrt{2688}=\sqrt{64*42}=\sqrt{64}*\sqrt{42}=8\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{42}}{2*4}=\frac{0-8\sqrt{42}}{8}
=-\frac{8\sqrt{42}}{8}
=-\sqrt{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{42}}{2*4}=\frac{0+8\sqrt{42}}{8}
=\frac{8\sqrt{42}}{8}
=\sqrt{42}
$