7x-2=5/6x-4

Solution for 7x-2=5/6x-4 equation:

7x-2=5/6x-4

We move all terms to the left:

7x-2-(5/6x-4)=0


Domain of the equation: 6x-4)!=0

x∈R


We get rid of parentheses

7x-5/6x+4-2=0

We multiply all the terms by the denominator


7x*6x+4*6x-2*6x-5=0

Wy multiply elements

42x^2+24x-12x-5=0

We add all the numbers together, and all the variables

42x^2+12x-5=0

a = 42; b = 12; c = -5;
Δ = b2-4ac
Δ = 122-4·42·(-5)
Δ = 984
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:

$\sqrt{\Delta}=\sqrt{984}=\sqrt{4*246}=\sqrt{4}*\sqrt{246}=2\sqrt{246}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{246}}{2*42}=\frac{-12-2\sqrt{246}}{84}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{246}}{2*42}=\frac{-12+2\sqrt{246}}{84}
$