(5+x)(8+x)=100

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Solution for (5+x)(8+x)=100 equation:



(5+x)(8+x)=100
We move all terms to the left:
(5+x)(8+x)-(100)=0
We add all the numbers together, and all the variables
(x+5)(x+8)-100=0
We multiply parentheses ..
(+x^2+8x+5x+40)-100=0
We get rid of parentheses
x^2+8x+5x+40-100=0
We add all the numbers together, and all the variables
x^2+13x-60=0
a = 1; b = 13; c = -60;
Δ = b2-4ac
Δ = 132-4·1·(-60)
Δ = 409
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{-(13)-\sqrt{409}}{2*1}=\frac{-13-\sqrt{409}}{2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{409}}{2*1}=\frac{-13+\sqrt{409}}{2} $

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