-10x-47=-x^2+1

Solution for -10x-47=-x^2+1 equation:

-10x-47=-x^2+1

We move all terms to the left:

-10x-47-(-x^2+1)=0

We get rid of parentheses

x^2-10x-1-47=0

We add all the numbers together, and all the variables

x^2-10x-48=0

a = 1; b = -10; c = -48;
Δ = b2-4ac
Δ = -102-4·1·(-48)
Δ = 292
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:

$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{73}}{2*1}=\frac{10-2\sqrt{73}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{73}}{2*1}=\frac{10+2\sqrt{73}}{2}
$