5x^2-3=2400

Solution for 5x^2-3=2400 equation:

5x^2-3=2400

We move all terms to the left:

5x^2-3-(2400)=0

We add all the numbers together, and all the variables

5x^2-2403=0

a = 5; b = 0; c = -2403;
Δ = b2-4ac
Δ = 02-4·5·(-2403)
Δ = 48060
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:

$\sqrt{\Delta}=\sqrt{48060}=\sqrt{36*1335}=\sqrt{36}*\sqrt{1335}=6\sqrt{1335}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{1335}}{2*5}=\frac{0-6\sqrt{1335}}{10}
=-\frac{6\sqrt{1335}}{10}
=-\frac{3\sqrt{1335}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{1335}}{2*5}=\frac{0+6\sqrt{1335}}{10}
=\frac{6\sqrt{1335}}{10}
=\frac{3\sqrt{1335}}{5}
$