(X+6)(x-7)=-7

Solution for (X+6)(x-7)=-7 equation:

(X+6)(X-7)=-7

We move all terms to the left:

(X+6)(X-7)-(-7)=0

We add all the numbers together, and all the variables

(X+6)(X-7)+7=0

We multiply parentheses ..

(+X^2-7X+6X-42)+7=0

We get rid of parentheses

X^2-7X+6X-42+7=0

We add all the numbers together, and all the variables

X^2-1X-35=0

a = 1; b = -1; c = -35;
Δ = b2-4ac
Δ = -12-4·1·(-35)
Δ = 141
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{-(-1)-\sqrt{141}}{2*1}=\frac{1-\sqrt{141}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{141}}{2*1}=\frac{1+\sqrt{141}}{2}
$