5=2.4x^2

Solution for 5=2.4x^2 equation:

5=2.4x^2

We move all terms to the left:

5-(2.4x^2)=0

We get rid of parentheses

-2.4x^2+5=0

a = -2.4; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-2.4)·5
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{3}}{2*-2.4}=\frac{0-4\sqrt{3}}{-4.8}
=-\frac{4\sqrt{3}}{-4.8}
=-\frac{\sqrt{3}}{-1.2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{3}}{2*-2.4}=\frac{0+4\sqrt{3}}{-4.8}
=\frac{4\sqrt{3}}{-4.8}
=\frac{\sqrt{3}}{-1.2}
$