40x^2-21=0

Solution for 40x^2-21=0 equation:

40x^2-21=0

a = 40; b = 0; c = -21;
Δ = b2-4ac
Δ = 02-4·40·(-21)
Δ = 3360
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:

$\sqrt{\Delta}=\sqrt{3360}=\sqrt{16*210}=\sqrt{16}*\sqrt{210}=4\sqrt{210}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{210}}{2*40}=\frac{0-4\sqrt{210}}{80}
=-\frac{4\sqrt{210}}{80}
=-\frac{\sqrt{210}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{210}}{2*40}=\frac{0+4\sqrt{210}}{80}
=\frac{4\sqrt{210}}{80}
=\frac{\sqrt{210}}{20}
$