2x^2+10x-414=0

Solution for 2x^2+10x-414=0 equation:

2x^2+10x-414=0

a = 2; b = 10; c = -414;
Δ = b2-4ac
Δ = 102-4·2·(-414)
Δ = 3412
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:

$\sqrt{\Delta}=\sqrt{3412}=\sqrt{4*853}=\sqrt{4}*\sqrt{853}=2\sqrt{853}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{853}}{2*2}=\frac{-10-2\sqrt{853}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{853}}{2*2}=\frac{-10+2\sqrt{853}}{4}
$