5/6x-10-3x=-36

Solution for 5/6x-10-3x=-36 equation:

5/6x-10-3x=-36

We move all terms to the left:

5/6x-10-3x-(-36)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

-3x+5/6x+26=0

We multiply all the terms by the denominator


-3x*6x+26*6x+5=0

Wy multiply elements

-18x^2+156x+5=0

a = -18; b = 156; c = +5;
Δ = b2-4ac
Δ = 1562-4·(-18)·5
Δ = 24696
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:

$\sqrt{\Delta}=\sqrt{24696}=\sqrt{1764*14}=\sqrt{1764}*\sqrt{14}=42\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(156)-42\sqrt{14}}{2*-18}=\frac{-156-42\sqrt{14}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(156)+42\sqrt{14}}{2*-18}=\frac{-156+42\sqrt{14}}{-36}
$