(x+6)(x-3)=-7

Solution for (x+6)(x-3)=-7 equation:

(x+6)(x-3)=-7

We move all terms to the left:

(x+6)(x-3)-(-7)=0

We add all the numbers together, and all the variables

(x+6)(x-3)+7=0

We multiply parentheses ..

(+x^2-3x+6x-18)+7=0

We get rid of parentheses

x^2-3x+6x-18+7=0

We add all the numbers together, and all the variables

x^2+3x-11=0

a = 1; b = 3; c = -11;
Δ = b2-4ac
Δ = 32-4·1·(-11)
Δ = 53
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{-(3)-\sqrt{53}}{2*1}=\frac{-3-\sqrt{53}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{53}}{2*1}=\frac{-3+\sqrt{53}}{2}
$