8x^2-100=200

Solution for 8x^2-100=200 equation:

8x^2-100=200

We move all terms to the left:

8x^2-100-(200)=0

We add all the numbers together, and all the variables

8x^2-300=0

a = 8; b = 0; c = -300;
Δ = b2-4ac
Δ = 02-4·8·(-300)
Δ = 9600
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:

$\sqrt{\Delta}=\sqrt{9600}=\sqrt{1600*6}=\sqrt{1600}*\sqrt{6}=40\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{6}}{2*8}=\frac{0-40\sqrt{6}}{16}
=-\frac{40\sqrt{6}}{16}
=-\frac{5\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{6}}{2*8}=\frac{0+40\sqrt{6}}{16}
=\frac{40\sqrt{6}}{16}
=\frac{5\sqrt{6}}{2}
$