-10x^2-100x+160=0

Solution for -10x^2-100x+160=0 equation:

-10x^2-100x+160=0

a = -10; b = -100; c = +160;
Δ = b2-4ac
Δ = -1002-4·(-10)·160
Δ = 16400
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:

$\sqrt{\Delta}=\sqrt{16400}=\sqrt{400*41}=\sqrt{400}*\sqrt{41}=20\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-20\sqrt{41}}{2*-10}=\frac{100-20\sqrt{41}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+20\sqrt{41}}{2*-10}=\frac{100+20\sqrt{41}}{-20}
$