(X+5)(x-7)=x-2x-35

Solution for (X+5)(x-7)=x-2x-35 equation:

(X+5)(X-7)=X-2X-35

We move all terms to the left:

(X+5)(X-7)-(X-2X-35)=0

We add all the numbers together, and all the variables

(X+5)(X-7)-(-1X-35)=0

We get rid of parentheses

(X+5)(X-7)+1X+35=0

We multiply parentheses ..

(+X^2-7X+5X-35)+1X+35=0

We add all the numbers together, and all the variables

(+X^2-7X+5X-35)+X+35=0

We get rid of parentheses

X^2-7X+5X+X-35+35=0

We add all the numbers together, and all the variables

X^2-1X=0

a = 1; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·1·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*1}=\frac{0}{2}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*1}=\frac{2}{2}
=1
$