15y=y2-3

Solution for 15y=y2-3 equation:

15y=y2-3

We move all terms to the left:

15y-(y2-3)=0

We add all the numbers together, and all the variables

-(+y^2-3)+15y=0

We get rid of parentheses

-y^2+15y+3=0

We add all the numbers together, and all the variables

-1y^2+15y+3=0

a = -1; b = 15; c = +3;
Δ = b2-4ac
Δ = 152-4·(-1)·3
Δ = 237
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-\sqrt{237}}{2*-1}=\frac{-15-\sqrt{237}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{237}}{2*-1}=\frac{-15+\sqrt{237}}{-2}
$