64x^2+10000x-10000=0

Solution for 64x^2+10000x-10000=0 equation:

64x^2+10000x-10000=0

a = 64; b = 10000; c = -10000;
Δ = b2-4ac
Δ = 100002-4·64·(-10000)
Δ = 102560000
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:

$\sqrt{\Delta}=\sqrt{102560000}=\sqrt{160000*641}=\sqrt{160000}*\sqrt{641}=400\sqrt{641}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10000)-400\sqrt{641}}{2*64}=\frac{-10000-400\sqrt{641}}{128}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10000)+400\sqrt{641}}{2*64}=\frac{-10000+400\sqrt{641}}{128}
$