1000+2x^2=8000

Solution for 1000+2x^2=8000 equation:

1000+2x^2=8000

We move all terms to the left:

1000+2x^2-(8000)=0

We add all the numbers together, and all the variables

2x^2-7000=0

a = 2; b = 0; c = -7000;
Δ = b2-4ac
Δ = 02-4·2·(-7000)
Δ = 56000
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:

$\sqrt{\Delta}=\sqrt{56000}=\sqrt{1600*35}=\sqrt{1600}*\sqrt{35}=40\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{35}}{2*2}=\frac{0-40\sqrt{35}}{4}
=-\frac{40\sqrt{35}}{4}
=-10\sqrt{35}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{35}}{2*2}=\frac{0+40\sqrt{35}}{4}
=\frac{40\sqrt{35}}{4}
=10\sqrt{35}
$