-50(x^2-82-8)=0

Solution for -50(x^2-82-8)=0 equation:

-50(x^2-82-8)=0

We multiply parentheses

-50x^2+4100+400=0

We add all the numbers together, and all the variables

-50x^2+4500=0

a = -50; b = 0; c = +4500;
Δ = b2-4ac
Δ = 02-4·(-50)·4500
Δ = 900000
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:

$\sqrt{\Delta}=\sqrt{900000}=\sqrt{90000*10}=\sqrt{90000}*\sqrt{10}=300\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-300\sqrt{10}}{2*-50}=\frac{0-300\sqrt{10}}{-100}
=-\frac{300\sqrt{10}}{-100}
=-\frac{3\sqrt{10}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+300\sqrt{10}}{2*-50}=\frac{0+300\sqrt{10}}{-100}
=\frac{300\sqrt{10}}{-100}
=\frac{3\sqrt{10}}{-1}
$