2x(x+1)-5/3=16x

Solution for 2x(x+1)-5/3=16x equation:

2x(x+1)-5/3=16x

We move all terms to the left:

2x(x+1)-5/3-(16x)=0

We add all the numbers together, and all the variables

-16x+2x(x+1)-5/3=0

We multiply parentheses

2x^2-16x+2x-5/3=0

We multiply all the terms by the denominator


2x^2*3-16x*3+2x*3-5=0

Wy multiply elements

6x^2-48x+6x-5=0

We add all the numbers together, and all the variables

6x^2-42x-5=0

a = 6; b = -42; c = -5;
Δ = b2-4ac
Δ = -422-4·6·(-5)
Δ = 1884
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:

$\sqrt{\Delta}=\sqrt{1884}=\sqrt{4*471}=\sqrt{4}*\sqrt{471}=2\sqrt{471}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{471}}{2*6}=\frac{42-2\sqrt{471}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{471}}{2*6}=\frac{42+2\sqrt{471}}{12}
$