(360/y-3)(y+4)=360

Solution for (360/y-3)(y+4)=360 equation:

(360/y-3)(y+4)=360

We move all terms to the left:

(360/y-3)(y+4)-(360)=0


Domain of the equation: y-3)(y+4)!=0

y∈R


We multiply parentheses ..

(+360y^2+1440y-3y-12)-360=0

We get rid of parentheses

360y^2+1440y-3y-12-360=0

We add all the numbers together, and all the variables

360y^2+1437y-372=0

a = 360; b = 1437; c = -372;
Δ = b2-4ac
Δ = 14372-4·360·(-372)
Δ = 2600649
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:

$\sqrt{\Delta}=\sqrt{2600649}=\sqrt{9*288961}=\sqrt{9}*\sqrt{288961}=3\sqrt{288961}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1437)-3\sqrt{288961}}{2*360}=\frac{-1437-3\sqrt{288961}}{720}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1437)+3\sqrt{288961}}{2*360}=\frac{-1437+3\sqrt{288961}}{720}
$