-5x^2+200=50

Solution for -5x^2+200=50 equation:

-5x^2+200=50

We move all terms to the left:

-5x^2+200-(50)=0

We add all the numbers together, and all the variables

-5x^2+150=0

a = -5; b = 0; c = +150;
Δ = b2-4ac
Δ = 02-4·(-5)·150
Δ = 3000
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:

$\sqrt{\Delta}=\sqrt{3000}=\sqrt{100*30}=\sqrt{100}*\sqrt{30}=10\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{30}}{2*-5}=\frac{0-10\sqrt{30}}{-10}
=-\frac{10\sqrt{30}}{-10}
=-\frac{\sqrt{30}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{30}}{2*-5}=\frac{0+10\sqrt{30}}{-10}
=\frac{10\sqrt{30}}{-10}
=\frac{\sqrt{30}}{-1}
$