5/6X-2y=21

Solution for 5/6X-2y=21 equation:

5/6X-2X=21

We move all terms to the left:

5/6X-2X-(21)=0


Domain of the equation: 6X!=0

X!=0/6

X!=0

X∈R


We add all the numbers together, and all the variables

-2X+5/6X-21=0

We multiply all the terms by the denominator


-2X*6X-21*6X+5=0

Wy multiply elements

-12X^2-126X+5=0

a = -12; b = -126; c = +5;
Δ = b2-4ac
Δ = -1262-4·(-12)·5
Δ = 16116
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:

$\sqrt{\Delta}=\sqrt{16116}=\sqrt{4*4029}=\sqrt{4}*\sqrt{4029}=2\sqrt{4029}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-126)-2\sqrt{4029}}{2*-12}=\frac{126-2\sqrt{4029}}{-24}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-126)+2\sqrt{4029}}{2*-12}=\frac{126+2\sqrt{4029}}{-24}
$