-3(-7-x)=1/2)x+2)

Solution for -3(-7-x)=1/2)x+2) equation:

-3(-7-x)=1/2)x+2)

We move all terms to the left:

-3(-7-x)-(1/2)x+2))=0


Domain of the equation: 2)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-3(-1x-7)-(+1/2)x+2))=0

We add all the numbers together, and all the variables

-3(-1x-7)-(+1/2)x=0

We multiply parentheses

-x^2+3x+21=0

We add all the numbers together, and all the variables

-1x^2+3x+21=0

a = -1; b = 3; c = +21;
Δ = b2-4ac
Δ = 32-4·(-1)·21
Δ = 93
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{93}}{2*-1}=\frac{-3-\sqrt{93}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{93}}{2*-1}=\frac{-3+\sqrt{93}}{-2}
$