5x^2-1000=-125

Solution for 5x^2-1000=-125 equation:

5x^2-1000=-125

We move all terms to the left:

5x^2-1000-(-125)=0

We add all the numbers together, and all the variables

5x^2-875=0

a = 5; b = 0; c = -875;
Δ = b2-4ac
Δ = 02-4·5·(-875)
Δ = 17500
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:

$\sqrt{\Delta}=\sqrt{17500}=\sqrt{2500*7}=\sqrt{2500}*\sqrt{7}=50\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-50\sqrt{7}}{2*5}=\frac{0-50\sqrt{7}}{10}
=-\frac{50\sqrt{7}}{10}
=-5\sqrt{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+50\sqrt{7}}{2*5}=\frac{0+50\sqrt{7}}{10}
=\frac{50\sqrt{7}}{10}
=5\sqrt{7}
$