2y+2y+5/2y+7/2y=360

Solution for 2y+2y+5/2y+7/2y=360 equation:

2y+2y+5/2y+7/2y=360

We move all terms to the left:

2y+2y+5/2y+7/2y-(360)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

4y+5/2y+7/2y-360=0

We multiply all the terms by the denominator


4y*2y-360*2y+5+7=0

We add all the numbers together, and all the variables

4y*2y-360*2y+12=0

Wy multiply elements

8y^2-720y+12=0

a = 8; b = -720; c = +12;
Δ = b2-4ac
Δ = -7202-4·8·12
Δ = 518016
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:

$\sqrt{\Delta}=\sqrt{518016}=\sqrt{64*8094}=\sqrt{64}*\sqrt{8094}=8\sqrt{8094}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-720)-8\sqrt{8094}}{2*8}=\frac{720-8\sqrt{8094}}{16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-720)+8\sqrt{8094}}{2*8}=\frac{720+8\sqrt{8094}}{16}
$