5/2y+4=2y-1

Solution for 5/2y+4=2y-1 equation:

5/2y+4=2y-1

We move all terms to the left:

5/2y+4-(2y-1)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We get rid of parentheses

5/2y-2y+1+4=0

We multiply all the terms by the denominator


-2y*2y+1*2y+4*2y+5=0

Wy multiply elements

-4y^2+2y+8y+5=0

We add all the numbers together, and all the variables

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

a = -4; b = 10; c = +5;
Δ = b2-4ac
Δ = 102-4·(-4)·5
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-6\sqrt{5}}{2*-4}=\frac{-10-6\sqrt{5}}{-8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+6\sqrt{5}}{2*-4}=\frac{-10+6\sqrt{5}}{-8}
$