(x+20)(x-24)=7067

Solution for (x+20)(x-24)=7067 equation:

(x+20)(x-24)=7067

We move all terms to the left:

(x+20)(x-24)-(7067)=0

We multiply parentheses ..

(+x^2-24x+20x-480)-7067=0

We get rid of parentheses

x^2-24x+20x-480-7067=0

We add all the numbers together, and all the variables

x^2-4x-7547=0

a = 1; b = -4; c = -7547;
Δ = b2-4ac
Δ = -42-4·1·(-7547)
Δ = 30204
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{30204}=\sqrt{36*839}=\sqrt{36}*\sqrt{839}=6\sqrt{839}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-6\sqrt{839}}{2*1}=\frac{4-6\sqrt{839}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+6\sqrt{839}}{2*1}=\frac{4+6\sqrt{839}}{2}
$