2x^2-6x-234=0

Solution for 2x^2-6x-234=0 equation:

2x^2-6x-234=0

a = 2; b = -6; c = -234;
Δ = b2-4ac
Δ = -62-4·2·(-234)
Δ = 1908
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:

$\sqrt{\Delta}=\sqrt{1908}=\sqrt{36*53}=\sqrt{36}*\sqrt{53}=6\sqrt{53}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{53}}{2*2}=\frac{6-6\sqrt{53}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{53}}{2*2}=\frac{6+6\sqrt{53}}{4}
$