3.5=2x(5.8+x)

Solution for 3.5=2x(5.8+x) equation:

3.5=2x(5.8+x)

We move all terms to the left:

3.5-(2x(5.8+x))=0

We add all the numbers together, and all the variables

-(2x(x+5.8))+3.5=0


We calculate terms in parentheses: -(2x(x+5.8)), so:

2x(x+5.8)

We multiply parentheses

2x^2+11.6x

Back to the equation:

-(2x^2+11.6x)


We get rid of parentheses

-2x^2-11.6x+3.5=0

a = -2; b = -11.6; c = +3.5;
Δ = b2-4ac
Δ = -11.62-4·(-2)·3.5
Δ = 162.56
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{-(-11.6)-\sqrt{162.56}}{2*-2}=\frac{11.6-\sqrt{162.56}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11.6)+\sqrt{162.56}}{2*-2}=\frac{11.6+\sqrt{162.56}}{-4}
$