10/4y=2y-2

Solution for 10/4y=2y-2 equation:

10/4y=2y-2

We move all terms to the left:

10/4y-(2y-2)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R


We get rid of parentheses

10/4y-2y+2=0

We multiply all the terms by the denominator


-2y*4y+2*4y+10=0

Wy multiply elements

-8y^2+8y+10=0

a = -8; b = 8; c = +10;
Δ = b2-4ac
Δ = 82-4·(-8)·10
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{6}}{2*-8}=\frac{-8-8\sqrt{6}}{-16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{6}}{2*-8}=\frac{-8+8\sqrt{6}}{-16}
$