X+7-16/3x=12-7/3x

Solution for X+7-16/3x=12-7/3x equation:

X+7-16/3X=12-7/3X

We move all terms to the left:

X+7-16/3X-(12-7/3X)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R



Domain of the equation: 3X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X-16/3X-(-7/3X+12)+7=0

We get rid of parentheses

X-16/3X+7/3X-12+7=0

We multiply all the terms by the denominator


X*3X-12*3X+7*3X-16+7=0

We add all the numbers together, and all the variables

X*3X-12*3X+7*3X-9=0

Wy multiply elements

3X^2-36X+21X-9=0

We add all the numbers together, and all the variables

3X^2-15X-9=0

a = 3; b = -15; c = -9;
Δ = b2-4ac
Δ = -152-4·3·(-9)
Δ = 333
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:

$\sqrt{\Delta}=\sqrt{333}=\sqrt{9*37}=\sqrt{9}*\sqrt{37}=3\sqrt{37}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{37}}{2*3}=\frac{15-3\sqrt{37}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{37}}{2*3}=\frac{15+3\sqrt{37}}{6}
$