(21x+93)-3/21x+93=-3

Solution for (21x+93)-3/21x+93=-3 equation:

(21x+93)-3/21x+93=-3

We move all terms to the left:

(21x+93)-3/21x+93-(-3)=0


Domain of the equation: 21x!=0

x!=0/21

x!=0

x∈R


We add all the numbers together, and all the variables

(21x+93)-3/21x+96=0

We get rid of parentheses

21x-3/21x+93+96=0

We multiply all the terms by the denominator


21x*21x+93*21x+96*21x-3=0

Wy multiply elements

441x^2+1953x+2016x-3=0

We add all the numbers together, and all the variables

441x^2+3969x-3=0

a = 441; b = 3969; c = -3;
Δ = b2-4ac
Δ = 39692-4·441·(-3)
Δ = 15758253
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:

$\sqrt{\Delta}=\sqrt{15758253}=\sqrt{441*35733}=\sqrt{441}*\sqrt{35733}=21\sqrt{35733}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3969)-21\sqrt{35733}}{2*441}=\frac{-3969-21\sqrt{35733}}{882}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3969)+21\sqrt{35733}}{2*441}=\frac{-3969+21\sqrt{35733}}{882}
$