X-3=90/y+1

Solution for X-3=90/y+1 equation:

X-3=90/X+1

We move all terms to the left:

X-3-(90/X+1)=0


Domain of the equation: X+1)!=0

X∈R


We get rid of parentheses

X-90/X-1-3=0

We multiply all the terms by the denominator


X*X-1*X-3*X-90=0

We add all the numbers together, and all the variables

-4X+X*X-90=0

Wy multiply elements

X^2-4X-90=0

a = 1; b = -4; c = -90;
Δ = b2-4ac
Δ = -42-4·1·(-90)
Δ = 376
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{376}=\sqrt{4*94}=\sqrt{4}*\sqrt{94}=2\sqrt{94}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{94}}{2*1}=\frac{4-2\sqrt{94}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{94}}{2*1}=\frac{4+2\sqrt{94}}{2}
$