20(x^2-8)=40

Solution for 20(x^2-8)=40 equation:

20(x^2-8)=40

We move all terms to the left:

20(x^2-8)-(40)=0

We multiply parentheses

20x^2-160-40=0

We add all the numbers together, and all the variables

20x^2-200=0

a = 20; b = 0; c = -200;
Δ = b2-4ac
Δ = 02-4·20·(-200)
Δ = 16000
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:

$\sqrt{\Delta}=\sqrt{16000}=\sqrt{1600*10}=\sqrt{1600}*\sqrt{10}=40\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{10}}{2*20}=\frac{0-40\sqrt{10}}{40}
=-\frac{40\sqrt{10}}{40}
=-\sqrt{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{10}}{2*20}=\frac{0+40\sqrt{10}}{40}
=\frac{40\sqrt{10}}{40}
=\sqrt{10}
$