5y-5/2y=0

Solution for 5y-5/2y=0 equation:

5y-5/2y=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We multiply all the terms by the denominator


5y*2y-5=0

Wy multiply elements

10y^2-5=0

a = 10; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·10·(-5)
Δ = 200
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:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{2}}{2*10}=\frac{0-10\sqrt{2}}{20}
=-\frac{10\sqrt{2}}{20}
=-\frac{\sqrt{2}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{2}}{2*10}=\frac{0+10\sqrt{2}}{20}
=\frac{10\sqrt{2}}{20}
=\frac{\sqrt{2}}{2}
$