x=-x^2-5x+10

Solution for x=-x^2-5x+10 equation:

x=-x^2-5x+10

We move all terms to the left:

x-(-x^2-5x+10)=0

We get rid of parentheses

x^2+5x+x-10=0

We add all the numbers together, and all the variables

x^2+6x-10=0

a = 1; b = 6; c = -10;
Δ = b2-4ac
Δ = 62-4·1·(-10)
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{19}}{2*1}=\frac{-6-2\sqrt{19}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{19}}{2*1}=\frac{-6+2\sqrt{19}}{2}
$