7x^2-21x-54=0

Solution for 7x^2-21x-54=0 equation:

7x^2-21x-54=0

a = 7; b = -21; c = -54;
Δ = b2-4ac
Δ = -212-4·7·(-54)
Δ = 1953
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:

$\sqrt{\Delta}=\sqrt{1953}=\sqrt{9*217}=\sqrt{9}*\sqrt{217}=3\sqrt{217}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3\sqrt{217}}{2*7}=\frac{21-3\sqrt{217}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3\sqrt{217}}{2*7}=\frac{21+3\sqrt{217}}{14}
$