(2x+5)3x=180

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Solution for (2x+5)3x=180 equation:



(2x+5)3x=180
We move all terms to the left:
(2x+5)3x-(180)=0
We multiply parentheses
6x^2+15x-180=0
a = 6; b = 15; c = -180;
Δ = b2-4ac
Δ = 152-4·6·(-180)
Δ = 4545
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:
$\sqrt{\Delta}=\sqrt{4545}=\sqrt{9*505}=\sqrt{9}*\sqrt{505}=3\sqrt{505}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{505}}{2*6}=\frac{-15-3\sqrt{505}}{12} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{505}}{2*6}=\frac{-15+3\sqrt{505}}{12} $

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