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

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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 $

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