2x^2+14x-250=0

Solution for 2x^2+14x-250=0 equation:

2x^2+14x-250=0

a = 2; b = 14; c = -250;
Δ = b2-4ac
Δ = 142-4·2·(-250)
Δ = 2196
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:

$\sqrt{\Delta}=\sqrt{2196}=\sqrt{36*61}=\sqrt{36}*\sqrt{61}=6\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-6\sqrt{61}}{2*2}=\frac{-14-6\sqrt{61}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+6\sqrt{61}}{2*2}=\frac{-14+6\sqrt{61}}{4}
$