84=(4x+2)6x

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Solution for 84=(4x+2)6x equation:



84=(4x+2)6x
We move all terms to the left:
84-((4x+2)6x)=0
We calculate terms in parentheses: -((4x+2)6x), so:
(4x+2)6x
We multiply parentheses
24x^2+12x
Back to the equation:
-(24x^2+12x)
We get rid of parentheses
-24x^2-12x+84=0
a = -24; b = -12; c = +84;
Δ = b2-4ac
Δ = -122-4·(-24)·84
Δ = 8208
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:
$\sqrt{\Delta}=\sqrt{8208}=\sqrt{144*57}=\sqrt{144}*\sqrt{57}=12\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{57}}{2*-24}=\frac{12-12\sqrt{57}}{-48} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{57}}{2*-24}=\frac{12+12\sqrt{57}}{-48} $

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