4x^2-3=241

Solution for 4x^2-3=241 equation:

4x^2-3=241

We move all terms to the left:

4x^2-3-(241)=0

We add all the numbers together, and all the variables

4x^2-244=0

a = 4; b = 0; c = -244;
Δ = b2-4ac
Δ = 02-4·4·(-244)
Δ = 3904
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:

$\sqrt{\Delta}=\sqrt{3904}=\sqrt{64*61}=\sqrt{64}*\sqrt{61}=8\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{61}}{2*4}=\frac{0-8\sqrt{61}}{8}
=-\frac{8\sqrt{61}}{8}
=-\sqrt{61}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{61}}{2*4}=\frac{0+8\sqrt{61}}{8}
=\frac{8\sqrt{61}}{8}
=\sqrt{61}
$