-x^2+5x+50=x^2

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

-x^2+5x+50=x^2

We move all terms to the left:

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

determiningTheFunctionDomain
-x^2-x^2+5x+50=0

We add all the numbers together, and all the variables

-2x^2+5x+50=0

a = -2; b = 5; c = +50;
Δ = b2-4ac
Δ = 52-4·(-2)·50
Δ = 425
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:

$\sqrt{\Delta}=\sqrt{425}=\sqrt{25*17}=\sqrt{25}*\sqrt{17}=5\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5\sqrt{17}}{2*-2}=\frac{-5-5\sqrt{17}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5\sqrt{17}}{2*-2}=\frac{-5+5\sqrt{17}}{-4}
$