4x^2-2x-1440=0

Solution for 4x^2-2x-1440=0 equation:

4x^2-2x-1440=0

a = 4; b = -2; c = -1440;
Δ = b2-4ac
Δ = -22-4·4·(-1440)
Δ = 23044
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:

$\sqrt{\Delta}=\sqrt{23044}=\sqrt{4*5761}=\sqrt{4}*\sqrt{5761}=2\sqrt{5761}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{5761}}{2*4}=\frac{2-2\sqrt{5761}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{5761}}{2*4}=\frac{2+2\sqrt{5761}}{8}
$