750+5x^2=1000

Solution for 750+5x^2=1000 equation:

750+5x^2=1000

We move all terms to the left:

750+5x^2-(1000)=0

We add all the numbers together, and all the variables

5x^2-250=0

a = 5; b = 0; c = -250;
Δ = b2-4ac
Δ = 02-4·5·(-250)
Δ = 5000
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:

$\sqrt{\Delta}=\sqrt{5000}=\sqrt{2500*2}=\sqrt{2500}*\sqrt{2}=50\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-50\sqrt{2}}{2*5}=\frac{0-50\sqrt{2}}{10}
=-\frac{50\sqrt{2}}{10}
=-5\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+50\sqrt{2}}{2*5}=\frac{0+50\sqrt{2}}{10}
=\frac{50\sqrt{2}}{10}
=5\sqrt{2}
$