5/2y+5=3y

Solution for 5/2y+5=3y equation:

5/2y+5=3y

We move all terms to the left:

5/2y+5-(3y)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

-3y+5/2y+5=0

We multiply all the terms by the denominator


-3y*2y+5*2y+5=0

Wy multiply elements

-6y^2+10y+5=0

a = -6; b = 10; c = +5;
Δ = b2-4ac
Δ = 102-4·(-6)·5
Δ = 220
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:

$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{55}}{2*-6}=\frac{-10-2\sqrt{55}}{-12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{55}}{2*-6}=\frac{-10+2\sqrt{55}}{-12}
$