2x^2-12x-51=0

Solution for 2x^2-12x-51=0 equation:

2x^2-12x-51=0

a = 2; b = -12; c = -51;
Δ = b2-4ac
Δ = -122-4·2·(-51)
Δ = 552
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:

$\sqrt{\Delta}=\sqrt{552}=\sqrt{4*138}=\sqrt{4}*\sqrt{138}=2\sqrt{138}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{138}}{2*2}=\frac{12-2\sqrt{138}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{138}}{2*2}=\frac{12+2\sqrt{138}}{4}
$