3(5+x)2x=45

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Solution for 3(5+x)2x=45 equation:



3(5+x)2x=45
We move all terms to the left:
3(5+x)2x-(45)=0
We add all the numbers together, and all the variables
3(x+5)2x-45=0
We multiply parentheses
6x^2+30x-45=0
a = 6; b = 30; c = -45;
Δ = b2-4ac
Δ = 302-4·6·(-45)
Δ = 1980
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:
$\sqrt{\Delta}=\sqrt{1980}=\sqrt{36*55}=\sqrt{36}*\sqrt{55}=6\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-6\sqrt{55}}{2*6}=\frac{-30-6\sqrt{55}}{12} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+6\sqrt{55}}{2*6}=\frac{-30+6\sqrt{55}}{12} $

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