2x(x+4)=3.5

Solution for 2x(x+4)=3.5 equation:

2x(x+4)=3.5

We move all terms to the left:

2x(x+4)-(3.5)=0

We add all the numbers together, and all the variables

2x(x+4)-3.5=0

We multiply parentheses

2x^2+8x-3.5=0

a = 2; b = 8; c = -3.5;
Δ = b2-4ac
Δ = 82-4·2·(-3.5)
Δ = 92
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:

$\sqrt{\Delta}=\sqrt{92}=\sqrt{4*23}=\sqrt{4}*\sqrt{23}=2\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{23}}{2*2}=\frac{-8-2\sqrt{23}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{23}}{2*2}=\frac{-8+2\sqrt{23}}{4}
$