7/3y+8=5y

Solution for 7/3y+8=5y equation:

7/3y+8=5y

We move all terms to the left:

7/3y+8-(5y)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

-5y+7/3y+8=0

We multiply all the terms by the denominator


-5y*3y+8*3y+7=0

Wy multiply elements

-15y^2+24y+7=0

a = -15; b = 24; c = +7;
Δ = b2-4ac
Δ = 242-4·(-15)·7
Δ = 996
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:

$\sqrt{\Delta}=\sqrt{996}=\sqrt{4*249}=\sqrt{4}*\sqrt{249}=2\sqrt{249}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{249}}{2*-15}=\frac{-24-2\sqrt{249}}{-30}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{249}}{2*-15}=\frac{-24+2\sqrt{249}}{-30}
$