5-5x-x*x=0

Solution for 5-5x-x*x=0 equation:

5-5x-x*x=0

Wy multiply elements

-1x^2-5x+5=0

a = -1; b = -5; c = +5;
Δ = b2-4ac
Δ = -52-4·(-1)·5
Δ = 45
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:

$\sqrt{\Delta}=\sqrt{45}=\sqrt{9*5}=\sqrt{9}*\sqrt{5}=3\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3\sqrt{5}}{2*-1}=\frac{5-3\sqrt{5}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3\sqrt{5}}{2*-1}=\frac{5+3\sqrt{5}}{-2}
$