2x^2+54x-99=0

Solution for 2x^2+54x-99=0 equation:

2x^2+54x-99=0

a = 2; b = 54; c = -99;
Δ = b2-4ac
Δ = 542-4·2·(-99)
Δ = 3708
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:

$\sqrt{\Delta}=\sqrt{3708}=\sqrt{36*103}=\sqrt{36}*\sqrt{103}=6\sqrt{103}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-6\sqrt{103}}{2*2}=\frac{-54-6\sqrt{103}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+6\sqrt{103}}{2*2}=\frac{-54+6\sqrt{103}}{4}
$