(5/6x)+5=3x-21

Solution for (5/6x)+5=3x-21 equation:

(5/6x)+5=3x-21

We move all terms to the left:

(5/6x)+5-(3x-21)=0


Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+5/6x)-(3x-21)+5=0

We get rid of parentheses

5/6x-3x+21+5=0

We multiply all the terms by the denominator


-3x*6x+21*6x+5*6x+5=0

Wy multiply elements

-18x^2+126x+30x+5=0

We add all the numbers together, and all the variables

-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}
$