180=(2x+60)6x

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Solution for 180=(2x+60)6x equation:



180=(2x+60)6x
We move all terms to the left:
180-((2x+60)6x)=0
We calculate terms in parentheses: -((2x+60)6x), so:
(2x+60)6x
We multiply parentheses
12x^2+360x
Back to the equation:
-(12x^2+360x)
We get rid of parentheses
-12x^2-360x+180=0
a = -12; b = -360; c = +180;
Δ = b2-4ac
Δ = -3602-4·(-12)·180
Δ = 138240
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:
$\sqrt{\Delta}=\sqrt{138240}=\sqrt{9216*15}=\sqrt{9216}*\sqrt{15}=96\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-96\sqrt{15}}{2*-12}=\frac{360-96\sqrt{15}}{-24} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+96\sqrt{15}}{2*-12}=\frac{360+96\sqrt{15}}{-24} $

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