(x-7)(x+2)=7

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

(x-7)(x+2)=7

We move all terms to the left:

(x-7)(x+2)-(7)=0

We multiply parentheses ..

(+x^2+2x-7x-14)-7=0

We get rid of parentheses

x^2+2x-7x-14-7=0

We add all the numbers together, and all the variables

x^2-5x-21=0

a = 1; b = -5; c = -21;
Δ = b2-4ac
Δ = -52-4·1·(-21)
Δ = 109
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{-(-5)-\sqrt{109}}{2*1}=\frac{5-\sqrt{109}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{109}}{2*1}=\frac{5+\sqrt{109}}{2}
$