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

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

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

We move all terms to the left:

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

We multiply parentheses

12x^2-4x-(-5x-(x-2))=0


We calculate terms in parentheses: -(-5x-(x-2)), so:

-5x-(x-2)

We get rid of parentheses

-5x-x+2

We add all the numbers together, and all the variables

-6x+2

Back to the equation:

-(-6x+2)


We get rid of parentheses

12x^2-4x+6x-2=0

We add all the numbers together, and all the variables

12x^2+2x-2=0

a = 12; b = 2; c = -2;
Δ = b2-4ac
Δ = 22-4·12·(-2)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-10}{2*12}=\frac{-12}{24}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+10}{2*12}=\frac{8}{24}
=1/3
$