x^2-30x-2=-211

Solution for x^2-30x-2=-211 equation:

x^2-30x-2=-211

We move all terms to the left:

x^2-30x-2-(-211)=0

We add all the numbers together, and all the variables

x^2-30x+209=0

a = 1; b = -30; c = +209;
Δ = b2-4ac
Δ = -302-4·1·209
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-8}{2*1}=\frac{22}{2}
=11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+8}{2*1}=\frac{38}{2}
=19
$