X+5/6x=3x-7

Solution for X+5/6x=3x-7 equation:

X+5/6X=3X-7

We move all terms to the left:

X+5/6X-(3X-7)=0


Domain of the equation: 6X!=0

X!=0/6

X!=0

X∈R


We get rid of parentheses

X+5/6X-3X+7=0

We multiply all the terms by the denominator


X*6X-3X*6X+7*6X+5=0

Wy multiply elements

6X^2-18X^2+42X+5=0

We add all the numbers together, and all the variables

-12X^2+42X+5=0

a = -12; b = 42; c = +5;
Δ = b2-4ac
Δ = 422-4·(-12)·5
Δ = 2004
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:

$\sqrt{\Delta}=\sqrt{2004}=\sqrt{4*501}=\sqrt{4}*\sqrt{501}=2\sqrt{501}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-2\sqrt{501}}{2*-12}=\frac{-42-2\sqrt{501}}{-24}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+2\sqrt{501}}{2*-12}=\frac{-42+2\sqrt{501}}{-24}
$