3.5x-1/6x-26=13

Solution for 3.5x-1/6x-26=13 equation:

3.5x-1/6x-26=13

We move all terms to the left:

3.5x-1/6x-26-(13)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

3.5x-1/6x-39=0

We multiply all the terms by the denominator


(3.5x)*6x-39*6x-1=0

We add all the numbers together, and all the variables

(+3.5x)*6x-39*6x-1=0

We multiply parentheses

18x^2-39*6x-1=0

Wy multiply elements

18x^2-234x-1=0

a = 18; b = -234; c = -1;
Δ = b2-4ac
Δ = -2342-4·18·(-1)
Δ = 54828
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:

$\sqrt{\Delta}=\sqrt{54828}=\sqrt{36*1523}=\sqrt{36}*\sqrt{1523}=6\sqrt{1523}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-234)-6\sqrt{1523}}{2*18}=\frac{234-6\sqrt{1523}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-234)+6\sqrt{1523}}{2*18}=\frac{234+6\sqrt{1523}}{36}
$