5x^2-30x-54=0

Solution for 5x^2-30x-54=0 equation:

5x^2-30x-54=0

a = 5; b = -30; c = -54;
Δ = b2-4ac
Δ = -302-4·5·(-54)
Δ = 1980
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:

$\sqrt{\Delta}=\sqrt{1980}=\sqrt{36*55}=\sqrt{36}*\sqrt{55}=6\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-6\sqrt{55}}{2*5}=\frac{30-6\sqrt{55}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+6\sqrt{55}}{2*5}=\frac{30+6\sqrt{55}}{10}
$