2x^2-14x-249=0

Solution for 2x^2-14x-249=0 equation:

2x^2-14x-249=0

a = 2; b = -14; c = -249;
Δ = b2-4ac
Δ = -142-4·2·(-249)
Δ = 2188
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:

$\sqrt{\Delta}=\sqrt{2188}=\sqrt{4*547}=\sqrt{4}*\sqrt{547}=2\sqrt{547}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{547}}{2*2}=\frac{14-2\sqrt{547}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{547}}{2*2}=\frac{14+2\sqrt{547}}{4}
$