3.5x+2=x(x-0.5)

Solution for 3.5x+2=x(x-0.5) equation:

3.5x+2=x(x-0.5)

We move all terms to the left:

3.5x+2-(x(x-0.5))=0


We calculate terms in parentheses: -(x(x-0.5)), so:

x(x-0.5)

We multiply parentheses

x^2-0.5x

Back to the equation:

-(x^2-0.5x)


We get rid of parentheses

-x^2+3.5x+0.5x+2=0

We add all the numbers together, and all the variables

-1x^2+4x+2=0

a = -1; b = 4; c = +2;
Δ = b2-4ac
Δ = 42-4·(-1)·2
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{6}}{2*-1}=\frac{-4-2\sqrt{6}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{6}}{2*-1}=\frac{-4+2\sqrt{6}}{-2}
$