7/6x=8x-6

Solution for 7/6x=8x-6 equation:

7/6x=8x-6

We move all terms to the left:

7/6x-(8x-6)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We get rid of parentheses

7/6x-8x+6=0

We multiply all the terms by the denominator


-8x*6x+6*6x+7=0

Wy multiply elements

-48x^2+36x+7=0

a = -48; b = 36; c = +7;
Δ = b2-4ac
Δ = 362-4·(-48)·7
Δ = 2640
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:

$\sqrt{\Delta}=\sqrt{2640}=\sqrt{16*165}=\sqrt{16}*\sqrt{165}=4\sqrt{165}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-4\sqrt{165}}{2*-48}=\frac{-36-4\sqrt{165}}{-96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+4\sqrt{165}}{2*-48}=\frac{-36+4\sqrt{165}}{-96}
$