(3x+47)(4x+6)=180

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Solution for (3x+47)(4x+6)=180 equation:



(3x+47)(4x+6)=180
We move all terms to the left:
(3x+47)(4x+6)-(180)=0
We multiply parentheses ..
(+12x^2+18x+188x+282)-180=0
We get rid of parentheses
12x^2+18x+188x+282-180=0
We add all the numbers together, and all the variables
12x^2+206x+102=0
a = 12; b = 206; c = +102;
Δ = b2-4ac
Δ = 2062-4·12·102
Δ = 37540
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:
$\sqrt{\Delta}=\sqrt{37540}=\sqrt{4*9385}=\sqrt{4}*\sqrt{9385}=2\sqrt{9385}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(206)-2\sqrt{9385}}{2*12}=\frac{-206-2\sqrt{9385}}{24} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(206)+2\sqrt{9385}}{2*12}=\frac{-206+2\sqrt{9385}}{24} $

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