2x-5/6x=4

Solution for 2x-5/6x=4 equation:

2x-5/6x=4

We move all terms to the left:

2x-5/6x-(4)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We multiply all the terms by the denominator


2x*6x-4*6x-5=0

Wy multiply elements

12x^2-24x-5=0

a = 12; b = -24; c = -5;
Δ = b2-4ac
Δ = -242-4·12·(-5)
Δ = 816
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:

$\sqrt{\Delta}=\sqrt{816}=\sqrt{16*51}=\sqrt{16}*\sqrt{51}=4\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{51}}{2*12}=\frac{24-4\sqrt{51}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{51}}{2*12}=\frac{24+4\sqrt{51}}{24}
$