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

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}
$