3.5=x(x+3)

Solution for 3.5=x(x+3) equation:

3.5=x(x+3)

We move all terms to the left:

3.5-(x(x+3))=0


We calculate terms in parentheses: -(x(x+3)), so:

x(x+3)

We multiply parentheses

x^2+3x

Back to the equation:

-(x^2+3x)


We get rid of parentheses

-x^2-3x+3.5=0

We add all the numbers together, and all the variables

-1x^2-3x+3.5=0

a = -1; b = -3; c = +3.5;
Δ = b2-4ac
Δ = -32-4·(-1)·3.5
Δ = 23
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{23}}{2*-1}=\frac{3-\sqrt{23}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{23}}{2*-1}=\frac{3+\sqrt{23}}{-2}
$