x+12=7/6(x)

Solution for x+12=7/6(x) equation:

x+12=7/6(x)

We move all terms to the left:

x+12-(7/6(x))=0


Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(+7/6x)+12=0

We get rid of parentheses

x-7/6x+12=0

We multiply all the terms by the denominator


x*6x+12*6x-7=0

Wy multiply elements

6x^2+72x-7=0

a = 6; b = 72; c = -7;
Δ = b2-4ac
Δ = 722-4·6·(-7)
Δ = 5352
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:

$\sqrt{\Delta}=\sqrt{5352}=\sqrt{4*1338}=\sqrt{4}*\sqrt{1338}=2\sqrt{1338}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-2\sqrt{1338}}{2*6}=\frac{-72-2\sqrt{1338}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+2\sqrt{1338}}{2*6}=\frac{-72+2\sqrt{1338}}{12}
$