4x^2+3=289

Solution for 4x^2+3=289 equation:

4x^2+3=289

We move all terms to the left:

4x^2+3-(289)=0

We add all the numbers together, and all the variables

4x^2-286=0

a = 4; b = 0; c = -286;
Δ = b2-4ac
Δ = 02-4·4·(-286)
Δ = 4576
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:

$\sqrt{\Delta}=\sqrt{4576}=\sqrt{16*286}=\sqrt{16}*\sqrt{286}=4\sqrt{286}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{286}}{2*4}=\frac{0-4\sqrt{286}}{8}
=-\frac{4\sqrt{286}}{8}
=-\frac{\sqrt{286}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{286}}{2*4}=\frac{0+4\sqrt{286}}{8}
=\frac{4\sqrt{286}}{8}
=\frac{\sqrt{286}}{2}
$