2(x2+4x=452)

Solution for 2(x2+4x=452) equation:

2(x2+4x=452)

We move all terms to the left:

2(x2+4x-(452))=0

We add all the numbers together, and all the variables

2(+x^2+4x-452)=0

We multiply parentheses

2x^2+8x-904=0

a = 2; b = 8; c = -904;
Δ = b2-4ac
Δ = 82-4·2·(-904)
Δ = 7296
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:

$\sqrt{\Delta}=\sqrt{7296}=\sqrt{64*114}=\sqrt{64}*\sqrt{114}=8\sqrt{114}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{114}}{2*2}=\frac{-8-8\sqrt{114}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{114}}{2*2}=\frac{-8+8\sqrt{114}}{4}
$