2x^2-14x-312=0

Solution for 2x^2-14x-312=0 equation:

2x^2-14x-312=0

a = 2; b = -14; c = -312;
Δ = b2-4ac
Δ = -142-4·2·(-312)
Δ = 2692
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:

$\sqrt{\Delta}=\sqrt{2692}=\sqrt{4*673}=\sqrt{4}*\sqrt{673}=2\sqrt{673}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{673}}{2*2}=\frac{14-2\sqrt{673}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{673}}{2*2}=\frac{14+2\sqrt{673}}{4}
$