2x(x+4)=4.5

Solution for 2x(x+4)=4.5 equation:

2x(x+4)=4.5

We move all terms to the left:

2x(x+4)-(4.5)=0

We add all the numbers together, and all the variables

2x(x+4)-4.5=0

We multiply parentheses

2x^2+8x-4.5=0

a = 2; b = 8; c = -4.5;
Δ = b2-4ac
Δ = 82-4·2·(-4.5)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-10}{2*2}=\frac{-18}{4}
=-4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+10}{2*2}=\frac{2}{4}
=1/2
$