2(X^2+5x-414)=0

Solution for 2(X^2+5x-414)=0 equation:

2(X^2+5X-414)=0

We multiply parentheses

2X^2+10X-828=0

a = 2; b = 10; c = -828;
Δ = b2-4ac
Δ = 102-4·2·(-828)
Δ = 6724
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6724}=82$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-82}{2*2}=\frac{-92}{4}
=-23
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+82}{2*2}=\frac{72}{4}
=18
$