5x^2=40^2

Solution for 5x^2=40^2 equation:

5x^2=40^2

We move all terms to the left:

5x^2-(40^2)=0

We add all the numbers together, and all the variables

5x^2-1600=0

a = 5; b = 0; c = -1600;
Δ = b2-4ac
Δ = 02-4·5·(-1600)
Δ = 32000
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:

$\sqrt{\Delta}=\sqrt{32000}=\sqrt{6400*5}=\sqrt{6400}*\sqrt{5}=80\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-80\sqrt{5}}{2*5}=\frac{0-80\sqrt{5}}{10}
=-\frac{80\sqrt{5}}{10}
=-8\sqrt{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+80\sqrt{5}}{2*5}=\frac{0+80\sqrt{5}}{10}
=\frac{80\sqrt{5}}{10}
=8\sqrt{5}
$