2y=5/2X-1

Solution for 2y=5/2X-1 equation:

2y=5/2y-1

We move all terms to the left:

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


Domain of the equation: 2y-1)!=0

y∈R


We get rid of parentheses

2y-5/2y+1=0

We multiply all the terms by the denominator


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

Wy multiply elements

4y^2+2y-5=0

a = 4; b = 2; c = -5;
Δ = b2-4ac
Δ = 22-4·4·(-5)
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{21}}{2*4}=\frac{-2-2\sqrt{21}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{21}}{2*4}=\frac{-2+2\sqrt{21}}{8}
$