(2x^2)-78x-338=0

Solution for (2x^2)-78x-338=0 equation:

(2x^2)-78x-338=0

a = 2; b = -78; c = -338;
Δ = b2-4ac
Δ = -782-4·2·(-338)
Δ = 8788
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:

$\sqrt{\Delta}=\sqrt{8788}=\sqrt{676*13}=\sqrt{676}*\sqrt{13}=26\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-26\sqrt{13}}{2*2}=\frac{78-26\sqrt{13}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+26\sqrt{13}}{2*2}=\frac{78+26\sqrt{13}}{4}
$