8+10x-(x^2)=-1

Solution for 8+10x-(x^2)=-1 equation:

8+10x-(x^2)=-1

We move all terms to the left:

8+10x-(x^2)-(-1)=0

determiningTheFunctionDomain
-x^2+10x+8-(-1)=0

We add all the numbers together, and all the variables

-1x^2+10x+9=0

a = -1; b = 10; c = +9;
Δ = b2-4ac
Δ = 102-4·(-1)·9
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{34}}{2*-1}=\frac{-10-2\sqrt{34}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{34}}{2*-1}=\frac{-10+2\sqrt{34}}{-2}
$