(x+7)(14+x)=330

Solution for (x+7)(14+x)=330 equation:

(x+7)(14+x)=330

We move all terms to the left:

(x+7)(14+x)-(330)=0

We add all the numbers together, and all the variables

(x+7)(x+14)-330=0

We multiply parentheses ..

(+x^2+14x+7x+98)-330=0

We get rid of parentheses

x^2+14x+7x+98-330=0

We add all the numbers together, and all the variables

x^2+21x-232=0

a = 1; b = 21; c = -232;
Δ = b2-4ac
Δ = 212-4·1·(-232)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-37}{2*1}=\frac{-58}{2}
=-29
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+37}{2*1}=\frac{16}{2}
=8
$