2x(18+2x)+50=450

Solution for 2x(18+2x)+50=450 equation:

2x(18+2x)+50=450

We move all terms to the left:

2x(18+2x)+50-(450)=0

We add all the numbers together, and all the variables

2x(2x+18)+50-450=0

We add all the numbers together, and all the variables

2x(2x+18)-400=0

We multiply parentheses

4x^2+36x-400=0

a = 4; b = 36; c = -400;
Δ = b2-4ac
Δ = 362-4·4·(-400)
Δ = 7696
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:

$\sqrt{\Delta}=\sqrt{7696}=\sqrt{16*481}=\sqrt{16}*\sqrt{481}=4\sqrt{481}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-4\sqrt{481}}{2*4}=\frac{-36-4\sqrt{481}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+4\sqrt{481}}{2*4}=\frac{-36+4\sqrt{481}}{8}
$