x^2-30x-54=0

Solution for x^2-30x-54=0 equation:

x^2-30x-54=0

a = 1; b = -30; c = -54;
Δ = b2-4ac
Δ = -302-4·1·(-54)
Δ = 1116
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:

$\sqrt{\Delta}=\sqrt{1116}=\sqrt{36*31}=\sqrt{36}*\sqrt{31}=6\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-6\sqrt{31}}{2*1}=\frac{30-6\sqrt{31}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+6\sqrt{31}}{2*1}=\frac{30+6\sqrt{31}}{2}
$