40x2=8

Solution for 40x2=8 equation:

40x^2=8

We move all terms to the left:

40x^2-(8)=0

a = 40; b = 0; c = -8;
Δ = b2-4ac
Δ = 02-4·40·(-8)
Δ = 1280
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:

$\sqrt{\Delta}=\sqrt{1280}=\sqrt{256*5}=\sqrt{256}*\sqrt{5}=16\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{5}}{2*40}=\frac{0-16\sqrt{5}}{80}
=-\frac{16\sqrt{5}}{80}
=-\frac{\sqrt{5}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{5}}{2*40}=\frac{0+16\sqrt{5}}{80}
=\frac{16\sqrt{5}}{80}
=\frac{\sqrt{5}}{5}
$