(x-7)(x+4)=13

Solution for (x-7)(x+4)=13 equation:

(x-7)(x+4)=13

We move all terms to the left:

(x-7)(x+4)-(13)=0

We multiply parentheses ..

(+x^2+4x-7x-28)-13=0

We get rid of parentheses

x^2+4x-7x-28-13=0

We add all the numbers together, and all the variables

x^2-3x-41=0

a = 1; b = -3; c = -41;
Δ = b2-4ac
Δ = -32-4·1·(-41)
Δ = 173
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{173}}{2*1}=\frac{3-\sqrt{173}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{173}}{2*1}=\frac{3+\sqrt{173}}{2}
$