10(-x^2+16x-10)=0

Solution for 10(-x^2+16x-10)=0 equation:

10(-x^2+16x-10)=0

We multiply parentheses

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

a = -10; b = 160; c = -100;
Δ = b2-4ac
Δ = 1602-4·(-10)·(-100)
Δ = 21600
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:

$\sqrt{\Delta}=\sqrt{21600}=\sqrt{3600*6}=\sqrt{3600}*\sqrt{6}=60\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(160)-60\sqrt{6}}{2*-10}=\frac{-160-60\sqrt{6}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(160)+60\sqrt{6}}{2*-10}=\frac{-160+60\sqrt{6}}{-20}
$