y-7=1/4(2y)

Solution for y-7=1/4(2y) equation:

y-7=1/4(2y)

We move all terms to the left:

y-7-(1/4(2y))=0


Domain of the equation: 42y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

y-(+1/42y)-7=0

We get rid of parentheses

y-1/42y-7=0

We multiply all the terms by the denominator


y*42y-7*42y-1=0

Wy multiply elements

42y^2-294y-1=0

a = 42; b = -294; c = -1;
Δ = b2-4ac
Δ = -2942-4·42·(-1)
Δ = 86604
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:

$\sqrt{\Delta}=\sqrt{86604}=\sqrt{4*21651}=\sqrt{4}*\sqrt{21651}=2\sqrt{21651}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-294)-2\sqrt{21651}}{2*42}=\frac{294-2\sqrt{21651}}{84}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-294)+2\sqrt{21651}}{2*42}=\frac{294+2\sqrt{21651}}{84}
$