2x^2-342x-72=0

Solution for 2x^2-342x-72=0 equation:

2x^2-342x-72=0

a = 2; b = -342; c = -72;
Δ = b2-4ac
Δ = -3422-4·2·(-72)
Δ = 117540
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:

$\sqrt{\Delta}=\sqrt{117540}=\sqrt{36*3265}=\sqrt{36}*\sqrt{3265}=6\sqrt{3265}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-342)-6\sqrt{3265}}{2*2}=\frac{342-6\sqrt{3265}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-342)+6\sqrt{3265}}{2*2}=\frac{342+6\sqrt{3265}}{4}
$