5/6x-3=2x-5

Solution for 5/6x-3=2x-5 equation:

5/6x-3=2x-5

We move all terms to the left:

5/6x-3-(2x-5)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We get rid of parentheses

5/6x-2x+5-3=0

We multiply all the terms by the denominator


-2x*6x+5*6x-3*6x+5=0

Wy multiply elements

-12x^2+30x-18x+5=0

We add all the numbers together, and all the variables

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

a = -12; b = 12; c = +5;
Δ = b2-4ac
Δ = 122-4·(-12)·5
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-8\sqrt{6}}{2*-12}=\frac{-12-8\sqrt{6}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+8\sqrt{6}}{2*-12}=\frac{-12+8\sqrt{6}}{-24}
$