4x^2-3=361

Solution for 4x^2-3=361 equation:

4x^2-3=361

We move all terms to the left:

4x^2-3-(361)=0

We add all the numbers together, and all the variables

4x^2-364=0

a = 4; b = 0; c = -364;
Δ = b2-4ac
Δ = 02-4·4·(-364)
Δ = 5824
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:

$\sqrt{\Delta}=\sqrt{5824}=\sqrt{64*91}=\sqrt{64}*\sqrt{91}=8\sqrt{91}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{91}}{2*4}=\frac{0-8\sqrt{91}}{8}
=-\frac{8\sqrt{91}}{8}
=-\sqrt{91}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{91}}{2*4}=\frac{0+8\sqrt{91}}{8}
=\frac{8\sqrt{91}}{8}
=\sqrt{91}
$