900/y-2y=15

Solution for 900/y-2y=15 equation:

900/y-2y=15

We move all terms to the left:

900/y-2y-(15)=0


Domain of the equation: y!=0

y∈R


We add all the numbers together, and all the variables

-2y+900/y-15=0

We multiply all the terms by the denominator


-2y*y-15*y+900=0

We add all the numbers together, and all the variables

-15y-2y*y+900=0

Wy multiply elements

-2y^2-15y+900=0

a = -2; b = -15; c = +900;
Δ = b2-4ac
Δ = -152-4·(-2)·900
Δ = 7425
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:

$\sqrt{\Delta}=\sqrt{7425}=\sqrt{225*33}=\sqrt{225}*\sqrt{33}=15\sqrt{33}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15\sqrt{33}}{2*-2}=\frac{15-15\sqrt{33}}{-4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15\sqrt{33}}{2*-2}=\frac{15+15\sqrt{33}}{-4}
$