5(-6.1+4.8x)=-(3/2)(-16x+20)

Solution for 5(-6.1+4.8x)=-(3/2)(-16x+20) equation:

5(-6.1+4.8x)=-(3/2)(-16x+20)

We move all terms to the left:

5(-6.1+4.8x)-(-(3/2)(-16x+20))=0


Domain of the equation: 2)(-16x+20))!=0

x∈R


We add all the numbers together, and all the variables

5(4.8x-6.1)-(-(+3/2)(-16x+20))=0

We multiply parentheses

20x-(-(+3/2)(-16x+20))-30.5=0

We multiply parentheses ..

-(-(-48x^2+3/2*20))+20x-30.5=0

We multiply all the terms by the denominator


-(-(-48x^2+3+20x*2*20))-(30.5)*2*20))=0


We calculate terms in parentheses: -(-(-48x^2+3+20x*2*20)), so:

-(-48x^2+3+20x*2*20)

We get rid of parentheses

48x^2-20x*2*20-3

Wy multiply elements

48x^2-800x*2-3

Wy multiply elements

48x^2-1600x-3

Back to the equation:

-(48x^2-1600x-3)


We add all the numbers together, and all the variables

-(48x^2-1600x-3)=0

We get rid of parentheses

-48x^2+1600x+3=0

a = -48; b = 1600; c = +3;
Δ = b2-4ac
Δ = 16002-4·(-48)·3
Δ = 2560576
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:

$\sqrt{\Delta}=\sqrt{2560576}=\sqrt{64*40009}=\sqrt{64}*\sqrt{40009}=8\sqrt{40009}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1600)-8\sqrt{40009}}{2*-48}=\frac{-1600-8\sqrt{40009}}{-96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1600)+8\sqrt{40009}}{2*-48}=\frac{-1600+8\sqrt{40009}}{-96}
$