4*x^2-100*x-1000=0

Solution for 4*x^2-100*x-1000=0 equation:

4x^2-100x-1000=0

a = 4; b = -100; c = -1000;
Δ = b2-4ac
Δ = -1002-4·4·(-1000)
Δ = 26000
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:

$\sqrt{\Delta}=\sqrt{26000}=\sqrt{400*65}=\sqrt{400}*\sqrt{65}=20\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-20\sqrt{65}}{2*4}=\frac{100-20\sqrt{65}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+20\sqrt{65}}{2*4}=\frac{100+20\sqrt{65}}{8}
$