5/6x-4-6x+2=-3

Solution for 5/6x-4-6x+2=-3 equation:

5/6x-4-6x+2=-3

We move all terms to the left:

5/6x-4-6x+2-(-3)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

-6x+5/6x+1=0

We multiply all the terms by the denominator


-6x*6x+1*6x+5=0

Wy multiply elements

-36x^2+6x+5=0

a = -36; b = 6; c = +5;
Δ = b2-4ac
Δ = 62-4·(-36)·5
Δ = 756
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:

$\sqrt{\Delta}=\sqrt{756}=\sqrt{36*21}=\sqrt{36}*\sqrt{21}=6\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{21}}{2*-36}=\frac{-6-6\sqrt{21}}{-72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{21}}{2*-36}=\frac{-6+6\sqrt{21}}{-72}
$