5x+3x(2x-1)+2=5x(6x-4)

Solution for 5x+3x(2x-1)+2=5x(6x-4) equation:

5x+3x(2x-1)+2=5x(6x-4)

We move all terms to the left:

5x+3x(2x-1)+2-(5x(6x-4))=0

We multiply parentheses

6x^2+5x-3x-(5x(6x-4))+2=0


We calculate terms in parentheses: -(5x(6x-4)), so:

5x(6x-4)

We multiply parentheses

30x^2-20x

Back to the equation:

-(30x^2-20x)


We add all the numbers together, and all the variables

6x^2+2x-(30x^2-20x)+2=0

We get rid of parentheses

6x^2-30x^2+2x+20x+2=0

We add all the numbers together, and all the variables

-24x^2+22x+2=0

a = -24; b = 22; c = +2;
Δ = b2-4ac
Δ = 222-4·(-24)·2
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-26}{2*-24}=\frac{-48}{-48}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+26}{2*-24}=\frac{4}{-48}
=-1/12
$