4x^2-2.5=1440

Solution for 4x^2-2.5=1440 equation:

4x^2-2.5=1440

We move all terms to the left:

4x^2-2.5-(1440)=0

We add all the numbers together, and all the variables

4x^2-1442.5=0

a = 4; b = 0; c = -1442.5;
Δ = b2-4ac
Δ = 02-4·4·(-1442.5)
Δ = 23080
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:

$\sqrt{\Delta}=\sqrt{23080}=\sqrt{4*5770}=\sqrt{4}*\sqrt{5770}=2\sqrt{5770}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{5770}}{2*4}=\frac{0-2\sqrt{5770}}{8}
=-\frac{2\sqrt{5770}}{8}
=-\frac{\sqrt{5770}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{5770}}{2*4}=\frac{0+2\sqrt{5770}}{8}
=\frac{2\sqrt{5770}}{8}
=\frac{\sqrt{5770}}{4}
$