(66+x)(40+x)=14300

Solution for (66+x)(40+x)=14300 equation:

(66+x)(40+x)=14300

We move all terms to the left:

(66+x)(40+x)-(14300)=0

We add all the numbers together, and all the variables

(x+66)(x+40)-14300=0

We multiply parentheses ..

(+x^2+40x+66x+2640)-14300=0

We get rid of parentheses

x^2+40x+66x+2640-14300=0

We add all the numbers together, and all the variables

x^2+106x-11660=0

a = 1; b = 106; c = -11660;
Δ = b2-4ac
Δ = 1062-4·1·(-11660)
Δ = 57876
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:

$\sqrt{\Delta}=\sqrt{57876}=\sqrt{4*14469}=\sqrt{4}*\sqrt{14469}=2\sqrt{14469}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(106)-2\sqrt{14469}}{2*1}=\frac{-106-2\sqrt{14469}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(106)+2\sqrt{14469}}{2*1}=\frac{-106+2\sqrt{14469}}{2}
$