-1527.78x^2+1000x+1000=0

Solution for -1527.78x^2+1000x+1000=0 equation:

-1527.78x^2+1000x+1000=0

a = -1527.78; b = 1000; c = +1000;
Δ = b2-4ac
Δ = 10002-4·(-1527.78)·1000
Δ = 7111120
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:

$\sqrt{\Delta}=\sqrt{7111120}=\sqrt{16*444445}=\sqrt{16}*\sqrt{444445}=4\sqrt{444445}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1000)-4\sqrt{444445}}{2*-1527.78}=\frac{-1000-4\sqrt{444445}}{-3055.56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1000)+4\sqrt{444445}}{2*-1527.78}=\frac{-1000+4\sqrt{444445}}{-3055.56}
$