5/4x-6(3x-9)=21

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Solution for 5/4x-6(3x-9)=21 equation:



5/4x-6(3x-9)=21
We move all terms to the left:
5/4x-6(3x-9)-(21)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
We multiply parentheses
5/4x-18x+54-21=0
We multiply all the terms by the denominator
-18x*4x+54*4x-21*4x+5=0
Wy multiply elements
-72x^2+216x-84x+5=0
We add all the numbers together, and all the variables
-72x^2+132x+5=0
a = -72; b = 132; c = +5;
Δ = b2-4ac
Δ = 1322-4·(-72)·5
Δ = 18864
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:
$\sqrt{\Delta}=\sqrt{18864}=\sqrt{144*131}=\sqrt{144}*\sqrt{131}=12\sqrt{131}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(132)-12\sqrt{131}}{2*-72}=\frac{-132-12\sqrt{131}}{-144} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(132)+12\sqrt{131}}{2*-72}=\frac{-132+12\sqrt{131}}{-144} $

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