4x^2-371=28

Solution for 4x^2-371=28 equation:

4x^2-371=28

We move all terms to the left:

4x^2-371-(28)=0

We add all the numbers together, and all the variables

4x^2-399=0

a = 4; b = 0; c = -399;
Δ = b2-4ac
Δ = 02-4·4·(-399)
Δ = 6384
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:

$\sqrt{\Delta}=\sqrt{6384}=\sqrt{16*399}=\sqrt{16}*\sqrt{399}=4\sqrt{399}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{399}}{2*4}=\frac{0-4\sqrt{399}}{8}
=-\frac{4\sqrt{399}}{8}
=-\frac{\sqrt{399}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{399}}{2*4}=\frac{0+4\sqrt{399}}{8}
=\frac{4\sqrt{399}}{8}
=\frac{\sqrt{399}}{2}
$