(12+2x)(8+2x)=36

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Solution for (12+2x)(8+2x)=36 equation:



(12+2x)(8+2x)=36
We move all terms to the left:
(12+2x)(8+2x)-(36)=0
We add all the numbers together, and all the variables
(2x+12)(2x+8)-36=0
We multiply parentheses ..
(+4x^2+16x+24x+96)-36=0
We get rid of parentheses
4x^2+16x+24x+96-36=0
We add all the numbers together, and all the variables
4x^2+40x+60=0
a = 4; b = 40; c = +60;
Δ = b2-4ac
Δ = 402-4·4·60
Δ = 640
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-8\sqrt{10}}{2*4}=\frac{-40-8\sqrt{10}}{8} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+8\sqrt{10}}{2*4}=\frac{-40+8\sqrt{10}}{8} $

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