3.4y-6=1/4y+10

Solution for 3.4y-6=1/4y+10 equation:

3.4y-6=1/4y+10

We move all terms to the left:

3.4y-6-(1/4y+10)=0


Domain of the equation: 4y+10)!=0

y∈R


We get rid of parentheses

3.4y-1/4y-10-6=0

We multiply all the terms by the denominator


(3.4y)*4y-10*4y-6*4y-1=0

We add all the numbers together, and all the variables

(+3.4y)*4y-10*4y-6*4y-1=0

We multiply parentheses

12y^2-10*4y-6*4y-1=0

Wy multiply elements

12y^2-40y-24y-1=0

We add all the numbers together, and all the variables

12y^2-64y-1=0

a = 12; b = -64; c = -1;
Δ = b2-4ac
Δ = -642-4·12·(-1)
Δ = 4144
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:

$\sqrt{\Delta}=\sqrt{4144}=\sqrt{16*259}=\sqrt{16}*\sqrt{259}=4\sqrt{259}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-4\sqrt{259}}{2*12}=\frac{64-4\sqrt{259}}{24}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+4\sqrt{259}}{2*12}=\frac{64+4\sqrt{259}}{24}
$