6x(3x+2)=2x(10x-1)

Solution for 6x(3x+2)=2x(10x-1) equation:

6x(3x+2)=2x(10x-1)

We move all terms to the left:

6x(3x+2)-(2x(10x-1))=0

We multiply parentheses

18x^2+12x-(2x(10x-1))=0


We calculate terms in parentheses: -(2x(10x-1)), so:

2x(10x-1)

We multiply parentheses

20x^2-2x

Back to the equation:

-(20x^2-2x)


We get rid of parentheses

18x^2-20x^2+12x+2x=0

We add all the numbers together, and all the variables

-2x^2+14x=0

a = -2; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·(-2)·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*-2}=\frac{-28}{-4}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*-2}=\frac{0}{-4}
=0
$