2x(4x-138)=x(65+1836x)

Solution for 2x(4x-138)=x(65+1836x) equation:

2x(4x-138)=x(65+1836x)

We move all terms to the left:

2x(4x-138)-(x(65+1836x))=0

We add all the numbers together, and all the variables

2x(4x-138)-(x(1836x+65))=0

We multiply parentheses

8x^2-276x-(x(1836x+65))=0


We calculate terms in parentheses: -(x(1836x+65)), so:

x(1836x+65)

We multiply parentheses

1836x^2+65x

Back to the equation:

-(1836x^2+65x)


We get rid of parentheses

8x^2-1836x^2-276x-65x=0

We add all the numbers together, and all the variables

-1828x^2-341x=0

a = -1828; b = -341; c = 0;
Δ = b2-4ac
Δ = -3412-4·(-1828)·0
Δ = 116281
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{116281}=341$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-341)-341}{2*-1828}=\frac{0}{-3656}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-341)+341}{2*-1828}=\frac{682}{-3656}
=-341/1828
$