-6(3-x)=21-(7)/(2)x

Solution for -6(3-x)=21-(7)/(2)x equation:

-6(3-x)=21-(7)/(2)x

We move all terms to the left:

-6(3-x)-(21-(7)/(2)x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-6(-1x+3)-(-7/2x+21)=0

We multiply parentheses

6x-(-7/2x+21)-18=0

We get rid of parentheses

6x+7/2x-21-18=0

We multiply all the terms by the denominator


6x*2x-21*2x-18*2x+7=0

Wy multiply elements

12x^2-42x-36x+7=0

We add all the numbers together, and all the variables

12x^2-78x+7=0

a = 12; b = -78; c = +7;
Δ = b2-4ac
Δ = -782-4·12·7
Δ = 5748
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:

$\sqrt{\Delta}=\sqrt{5748}=\sqrt{4*1437}=\sqrt{4}*\sqrt{1437}=2\sqrt{1437}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-2\sqrt{1437}}{2*12}=\frac{78-2\sqrt{1437}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+2\sqrt{1437}}{2*12}=\frac{78+2\sqrt{1437}}{24}
$