(5+x)(x)=84

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Solution for (5+x)(x)=84 equation:



(5+x)(x)=84
We move all terms to the left:
(5+x)(x)-(84)=0
We add all the numbers together, and all the variables
(x+5)x-84=0
We multiply parentheses
x^2+5x-84=0
a = 1; b = 5; c = -84;
Δ = b2-4ac
Δ = 52-4·1·(-84)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-19}{2*1}=\frac{-24}{2} =-12 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+19}{2*1}=\frac{14}{2} =7 $

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