(66+x)(40+x)=2954.5

Solution for (66+x)(40+x)=2954.5 equation:

(66+x)(40+x)=2954.5

We move all terms to the left:

(66+x)(40+x)-(2954.5)=0

We add all the numbers together, and all the variables

(x+66)(x+40)-(2954.5)=0

We add all the numbers together, and all the variables

(x+66)(x+40)-2954.5=0

We multiply parentheses ..

(+x^2+40x+66x+2640)-2954.5=0

We get rid of parentheses

x^2+40x+66x+2640-2954.5=0

We add all the numbers together, and all the variables

x^2+106x-314.5=0

a = 1; b = 106; c = -314.5;
Δ = b2-4ac
Δ = 1062-4·1·(-314.5)
Δ = 12494
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{-(106)-\sqrt{12494}}{2*1}=\frac{-106-\sqrt{12494}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(106)+\sqrt{12494}}{2*1}=\frac{-106+\sqrt{12494}}{2}
$