-x+(3/2)(x+6)=3

Solution for -x+(3/2)(x+6)=3 equation:

-x+(3/2)(x+6)=3

We move all terms to the left:

-x+(3/2)(x+6)-(3)=0


Domain of the equation: 2)(x+6)!=0

x∈R


We add all the numbers together, and all the variables

-x+(+3/2)(x+6)-3=0

We add all the numbers together, and all the variables

-1x+(+3/2)(x+6)-3=0

We multiply parentheses ..

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

We get rid of parentheses

3x^2-1x*2*6+3=0

Wy multiply elements

3x^2-12x*6+3=0

Wy multiply elements

3x^2-72x+3=0

a = 3; b = -72; c = +3;
Δ = b2-4ac
Δ = -722-4·3·3
Δ = 5148
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:

$\sqrt{\Delta}=\sqrt{5148}=\sqrt{36*143}=\sqrt{36}*\sqrt{143}=6\sqrt{143}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-6\sqrt{143}}{2*3}=\frac{72-6\sqrt{143}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+6\sqrt{143}}{2*3}=\frac{72+6\sqrt{143}}{6}
$