5+1/2y=2y-2.5

Solution for 5+1/2y=2y-2.5 equation:

5+1/2y=2y-2.5

We move all terms to the left:

5+1/2y-(2y-2.5)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We get rid of parentheses

1/2y-2y+2.5+5=0

We multiply all the terms by the denominator


-2y*2y+(2.5)*2y+5*2y+1=0

We multiply parentheses

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

Wy multiply elements

-4y^2+5y+10y+1=0

We add all the numbers together, and all the variables

-4y^2+15y+1=0

a = -4; b = 15; c = +1;
Δ = b2-4ac
Δ = 152-4·(-4)·1
Δ = 241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-\sqrt{241}}{2*-4}=\frac{-15-\sqrt{241}}{-8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{241}}{2*-4}=\frac{-15+\sqrt{241}}{-8}
$