2y+10=5/4y

Solution for 2y+10=5/4y equation:

2y+10=5/4y

We move all terms to the left:

2y+10-(5/4y)=0


Domain of the equation: 4y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

2y-(+5/4y)+10=0

We get rid of parentheses

2y-5/4y+10=0

We multiply all the terms by the denominator


2y*4y+10*4y-5=0

Wy multiply elements

8y^2+40y-5=0

a = 8; b = 40; c = -5;
Δ = b2-4ac
Δ = 402-4·8·(-5)
Δ = 1760
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:

$\sqrt{\Delta}=\sqrt{1760}=\sqrt{16*110}=\sqrt{16}*\sqrt{110}=4\sqrt{110}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-4\sqrt{110}}{2*8}=\frac{-40-4\sqrt{110}}{16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+4\sqrt{110}}{2*8}=\frac{-40+4\sqrt{110}}{16}
$