7/4y=y

Solution for 7/4y=y equation:

7/4y=y

We move all terms to the left:

7/4y-(y)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R


We add all the numbers together, and all the variables

-1y+7/4y=0

We multiply all the terms by the denominator


-1y*4y+7=0

Wy multiply elements

-4y^2+7=0

a = -4; b = 0; c = +7;
Δ = b2-4ac
Δ = 02-4·(-4)·7
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{7}}{2*-4}=\frac{0-4\sqrt{7}}{-8}
=-\frac{4\sqrt{7}}{-8}
=-\frac{\sqrt{7}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{7}}{2*-4}=\frac{0+4\sqrt{7}}{-8}
=\frac{4\sqrt{7}}{-8}
=\frac{\sqrt{7}}{-2}
$