x^2-30x+200=-21

Solution for x^2-30x+200=-21 equation:

x^2-30x+200=-21

We move all terms to the left:

x^2-30x+200-(-21)=0

We add all the numbers together, and all the variables

x^2-30x+221=0

a = 1; b = -30; c = +221;
Δ = b2-4ac
Δ = -302-4·1·221
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-4}{2*1}=\frac{26}{2}
=13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+4}{2*1}=\frac{34}{2}
=17
$