5/6x=2x-7

Solution for 5/6x=2x-7 equation:

5/6x=2x-7

We move all terms to the left:

5/6x-(2x-7)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We get rid of parentheses

5/6x-2x+7=0

We multiply all the terms by the denominator


-2x*6x+7*6x+5=0

Wy multiply elements

-12x^2+42x+5=0

a = -12; b = 42; c = +5;
Δ = b2-4ac
Δ = 422-4·(-12)·5
Δ = 2004
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:

$\sqrt{\Delta}=\sqrt{2004}=\sqrt{4*501}=\sqrt{4}*\sqrt{501}=2\sqrt{501}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-2\sqrt{501}}{2*-12}=\frac{-42-2\sqrt{501}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+2\sqrt{501}}{2*-12}=\frac{-42+2\sqrt{501}}{-24}
$