8/6x-136=5x

Solution for 8/6x-136=5x equation:

8/6x-136=5x

We move all terms to the left:

8/6x-136-(5x)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

-5x+8/6x-136=0

We multiply all the terms by the denominator


-5x*6x-136*6x+8=0

Wy multiply elements

-30x^2-816x+8=0

a = -30; b = -816; c = +8;
Δ = b2-4ac
Δ = -8162-4·(-30)·8
Δ = 666816
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:

$\sqrt{\Delta}=\sqrt{666816}=\sqrt{64*10419}=\sqrt{64}*\sqrt{10419}=8\sqrt{10419}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-816)-8\sqrt{10419}}{2*-30}=\frac{816-8\sqrt{10419}}{-60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-816)+8\sqrt{10419}}{2*-30}=\frac{816+8\sqrt{10419}}{-60}
$