30-10x-x2=0

Solution for 30-10x-x2=0 equation:

30-10x-x2=0

We add all the numbers together, and all the variables

-1x^2-10x+30=0

a = -1; b = -10; c = +30;
Δ = b2-4ac
Δ = -102-4·(-1)·30
Δ = 220
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:

$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{55}}{2*-1}=\frac{10-2\sqrt{55}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{55}}{2*-1}=\frac{10+2\sqrt{55}}{-2}
$