7/2y=7y+4

Solution for 7/2y=7y+4 equation:

7/2y=7y+4

We move all terms to the left:

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


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We get rid of parentheses

7/2y-7y-4=0

We multiply all the terms by the denominator


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

Wy multiply elements

-14y^2-8y+7=0

a = -14; b = -8; c = +7;
Δ = b2-4ac
Δ = -82-4·(-14)·7
Δ = 456
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:

$\sqrt{\Delta}=\sqrt{456}=\sqrt{4*114}=\sqrt{4}*\sqrt{114}=2\sqrt{114}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{114}}{2*-14}=\frac{8-2\sqrt{114}}{-28}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{114}}{2*-14}=\frac{8+2\sqrt{114}}{-28}
$