2-5/2y-y=9

Solution for 2-5/2y-y=9 equation:

2-5/2y-y=9

We move all terms to the left:

2-5/2y-y-(9)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

-1y-5/2y-7=0

We multiply all the terms by the denominator


-1y*2y-7*2y-5=0

Wy multiply elements

-2y^2-14y-5=0

a = -2; b = -14; c = -5;
Δ = b2-4ac
Δ = -142-4·(-2)·(-5)
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{39}}{2*-2}=\frac{14-2\sqrt{39}}{-4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{39}}{2*-2}=\frac{14+2\sqrt{39}}{-4}
$