9x^2+54x-57=0

Solution for 9x^2+54x-57=0 equation:

9x^2+54x-57=0

a = 9; b = 54; c = -57;
Δ = b2-4ac
Δ = 542-4·9·(-57)
Δ = 4968
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:

$\sqrt{\Delta}=\sqrt{4968}=\sqrt{36*138}=\sqrt{36}*\sqrt{138}=6\sqrt{138}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-6\sqrt{138}}{2*9}=\frac{-54-6\sqrt{138}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+6\sqrt{138}}{2*9}=\frac{-54+6\sqrt{138}}{18}
$