(x-1)(x+1)=21x-3

Solution for (x-1)(x+1)=21x-3 equation:

(x-1)(x+1)=21x-3

We move all terms to the left:

(x-1)(x+1)-(21x-3)=0

We use the square of the difference formula

x^2-(21x-3)-1=0

We get rid of parentheses

x^2-21x+3-1=0

We add all the numbers together, and all the variables

x^2-21x+2=0

a = 1; b = -21; c = +2;
Δ = b2-4ac
Δ = -212-4·1·2
Δ = 433
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-\sqrt{433}}{2*1}=\frac{21-\sqrt{433}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{433}}{2*1}=\frac{21+\sqrt{433}}{2}
$