(3X+7)/6=6X/e

Solution for (3X+7)/6=6X/e equation:

(3X+7)/6=6X/X

We move all terms to the left:

(3X+7)/6-(6X/X)=0


Domain of the equation: X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

(3X+7)/6-(+6X/X)=0

We get rid of parentheses

(3X+7)/6-6X/X=0

We calculate fractions


(3X^2+7X)/6X+(-36X)/6X=0

We multiply all the terms by the denominator


(3X^2+7X)+(-36X)=0

We get rid of parentheses

3X^2+7X-36X=0

We add all the numbers together, and all the variables

3X^2-29X=0

a = 3; b = -29; c = 0;
Δ = b2-4ac
Δ = -292-4·3·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-29}{2*3}=\frac{0}{6}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+29}{2*3}=\frac{58}{6}
=9+2/3
$