(x+10)(x+14)=280

Solution for (x+10)(x+14)=280 equation:

(x+10)(x+14)=280

We move all terms to the left:

(x+10)(x+14)-(280)=0

We multiply parentheses ..

(+x^2+14x+10x+140)-280=0

We get rid of parentheses

x^2+14x+10x+140-280=0

We add all the numbers together, and all the variables

x^2+24x-140=0

a = 1; b = 24; c = -140;
Δ = b2-4ac
Δ = 242-4·1·(-140)
Δ = 1136
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:

$\sqrt{\Delta}=\sqrt{1136}=\sqrt{16*71}=\sqrt{16}*\sqrt{71}=4\sqrt{71}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{71}}{2*1}=\frac{-24-4\sqrt{71}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{71}}{2*1}=\frac{-24+4\sqrt{71}}{2}
$