4x^2+7x-1/1000=0

Solution for 4x^2+7x-1/1000=0 equation:

4x^2+7x-1/1000=0

We multiply all the terms by the denominator


4x^2*1000+7x*1000-1=0

Wy multiply elements

4000x^2+7000x-1=0

a = 4000; b = 7000; c = -1;
Δ = b2-4ac
Δ = 70002-4·4000·(-1)
Δ = 49016000
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:

$\sqrt{\Delta}=\sqrt{49016000}=\sqrt{1600*30635}=\sqrt{1600}*\sqrt{30635}=40\sqrt{30635}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7000)-40\sqrt{30635}}{2*4000}=\frac{-7000-40\sqrt{30635}}{8000}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7000)+40\sqrt{30635}}{2*4000}=\frac{-7000+40\sqrt{30635}}{8000}
$