X=5/6v+2

Solution for X=5/6v+2 equation:

X=5/6X+2

We move all terms to the left:

X-(5/6X+2)=0


Domain of the equation: 6X+2)!=0

X∈R


We get rid of parentheses

X-5/6X-2=0

We multiply all the terms by the denominator


X*6X-2*6X-5=0

Wy multiply elements

6X^2-12X-5=0

a = 6; b = -12; c = -5;
Δ = b2-4ac
Δ = -122-4·6·(-5)
Δ = 264
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:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{66}}{2*6}=\frac{12-2\sqrt{66}}{12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{66}}{2*6}=\frac{12+2\sqrt{66}}{12}
$