9(5-3x)=(2/4)(x+4)

Solution for 9(5-3x)=(2/4)(x+4) equation:

9(5-3x)=(2/4)(x+4)

We move all terms to the left:

9(5-3x)-((2/4)(x+4))=0


Domain of the equation: 4)(x+4))!=0

x∈R


We add all the numbers together, and all the variables

9(-3x+5)-((+2/4)(x+4))=0

We multiply parentheses

-27x-((+2/4)(x+4))+45=0

We multiply parentheses ..

-((+2x^2+2/4*4))-27x+45=0

We multiply all the terms by the denominator


-((+2x^2+2-27x*4*4))+45*4*4))=0


We calculate terms in parentheses: -((+2x^2+2-27x*4*4)), so:

(+2x^2+2-27x*4*4)

We get rid of parentheses

2x^2-27x*4*4+2

Wy multiply elements

2x^2-432x*4+2

Wy multiply elements

2x^2-1728x+2

Back to the equation:

-(2x^2-1728x+2)


We add all the numbers together, and all the variables

-(2x^2-1728x+2)=0

We get rid of parentheses

-2x^2+1728x-2=0

a = -2; b = 1728; c = -2;
Δ = b2-4ac
Δ = 17282-4·(-2)·(-2)
Δ = 2985968
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:

$\sqrt{\Delta}=\sqrt{2985968}=\sqrt{16*186623}=\sqrt{16}*\sqrt{186623}=4\sqrt{186623}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1728)-4\sqrt{186623}}{2*-2}=\frac{-1728-4\sqrt{186623}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1728)+4\sqrt{186623}}{2*-2}=\frac{-1728+4\sqrt{186623}}{-4}
$