(x+40)(x-10)=260

Solution for (x+40)(x-10)=260 equation:

(x+40)(x-10)=260

We move all terms to the left:

(x+40)(x-10)-(260)=0

We multiply parentheses ..

(+x^2-10x+40x-400)-260=0

We get rid of parentheses

x^2-10x+40x-400-260=0

We add all the numbers together, and all the variables

x^2+30x-660=0

a = 1; b = 30; c = -660;
Δ = b2-4ac
Δ = 302-4·1·(-660)
Δ = 3540
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:

$\sqrt{\Delta}=\sqrt{3540}=\sqrt{4*885}=\sqrt{4}*\sqrt{885}=2\sqrt{885}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{885}}{2*1}=\frac{-30-2\sqrt{885}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{885}}{2*1}=\frac{-30+2\sqrt{885}}{2}
$