4/7y-2=4y-6

Solution for 4/7y-2=4y-6 equation:

4/7y-2=4y-6

We move all terms to the left:

4/7y-2-(4y-6)=0


Domain of the equation: 7y!=0

y!=0/7

y!=0

y∈R


We get rid of parentheses

4/7y-4y+6-2=0

We multiply all the terms by the denominator


-4y*7y+6*7y-2*7y+4=0

Wy multiply elements

-28y^2+42y-14y+4=0

We add all the numbers together, and all the variables

-28y^2+28y+4=0

a = -28; b = 28; c = +4;
Δ = b2-4ac
Δ = 282-4·(-28)·4
Δ = 1232
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1232}=\sqrt{16*77}=\sqrt{16}*\sqrt{77}=4\sqrt{77}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-4\sqrt{77}}{2*-28}=\frac{-28-4\sqrt{77}}{-56}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+4\sqrt{77}}{2*-28}=\frac{-28+4\sqrt{77}}{-56}
$