(X-3)(2x+7)=x^2-1

Solution for (X-3)(2x+7)=x^2-1 equation:

(X-3)(2X+7)=X^2-1

We move all terms to the left:

(X-3)(2X+7)-(X^2-1)=0

We get rid of parentheses

-X^2+(X-3)(2X+7)+1=0

We multiply parentheses ..

-X^2+(+2X^2+7X-6X-21)+1=0

We add all the numbers together, and all the variables

-1X^2+(+2X^2+7X-6X-21)+1=0

We get rid of parentheses

-1X^2+2X^2+7X-6X-21+1=0

We add all the numbers together, and all the variables

X^2+X-20=0

a = 1; b = 1; c = -20;
Δ = b2-4ac
Δ = 12-4·1·(-20)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-9}{2*1}=\frac{-10}{2}
=-5
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+9}{2*1}=\frac{8}{2}
=4
$