x2-30x+213=0

Solution for x2-30x+213=0 equation:

x2-30x+213=0

We add all the numbers together, and all the variables

x^2-30x+213=0

a = 1; b = -30; c = +213;
Δ = b2-4ac
Δ = -302-4·1·213
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-4\sqrt{3}}{2*1}=\frac{30-4\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+4\sqrt{3}}{2*1}=\frac{30+4\sqrt{3}}{2}
$