X+5/6x=7

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

X+5/6X=7

We move all terms to the left:

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


Domain of the equation: 6X!=0

X!=0/6

X!=0

X∈R


We multiply all the terms by the denominator


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

Wy multiply elements

6X^2-42X+5=0

a = 6; b = -42; c = +5;
Δ = b2-4ac
Δ = -422-4·6·5
Δ = 1644
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:

$\sqrt{\Delta}=\sqrt{1644}=\sqrt{4*411}=\sqrt{4}*\sqrt{411}=2\sqrt{411}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{411}}{2*6}=\frac{42-2\sqrt{411}}{12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{411}}{2*6}=\frac{42+2\sqrt{411}}{12}
$