-9/2y-2y=-52

Solution for -9/2y-2y=-52 equation:

-9/2y-2y=-52

We move all terms to the left:

-9/2y-2y-(-52)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

-2y-9/2y+52=0

We multiply all the terms by the denominator


-2y*2y+52*2y-9=0

Wy multiply elements

-4y^2+104y-9=0

a = -4; b = 104; c = -9;
Δ = b2-4ac
Δ = 1042-4·(-4)·(-9)
Δ = 10672
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:

$\sqrt{\Delta}=\sqrt{10672}=\sqrt{16*667}=\sqrt{16}*\sqrt{667}=4\sqrt{667}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(104)-4\sqrt{667}}{2*-4}=\frac{-104-4\sqrt{667}}{-8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(104)+4\sqrt{667}}{2*-4}=\frac{-104+4\sqrt{667}}{-8}
$