.5(x+2)=(.5x+2)(x-3)

Solution for .5(x+2)=(.5x+2)(x-3) equation:

.5(x+2)=(.5x+2)(x-3)

We move all terms to the left:

.5(x+2)-((.5x+2)(x-3))=0

We multiply parentheses

0.5x-((.5x+2)(x-3))+1=0

We multiply parentheses ..

-((+x^2-3x+2x-6))+0.5x+1=0


We calculate terms in parentheses: -((+x^2-3x+2x-6)), so:

(+x^2-3x+2x-6)

We get rid of parentheses

x^2-3x+2x-6

We add all the numbers together, and all the variables

x^2-1x-6

Back to the equation:

-(x^2-1x-6)


We add all the numbers together, and all the variables

0.5x-(x^2-1x-6)+1=0

We get rid of parentheses

-x^2+0.5x+1x+6+1=0

We add all the numbers together, and all the variables

-1x^2+1.5x+7=0

a = -1; b = 1.5; c = +7;
Δ = b2-4ac
Δ = 1.52-4·(-1)·7
Δ = 30.25
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{-(1.5)-\sqrt{30.25}}{2*-1}=\frac{-1.5-\sqrt{30.25}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.5)+\sqrt{30.25}}{2*-1}=\frac{-1.5+\sqrt{30.25}}{-2}
$