4x(3x-1)=6-(21x+3)

Solution for 4x(3x-1)=6-(21x+3) equation:

4x(3x-1)=6-(21x+3)

We move all terms to the left:

4x(3x-1)-(6-(21x+3))=0

We multiply parentheses

12x^2-4x-(6-(21x+3))=0


We calculate terms in parentheses: -(6-(21x+3)), so:

6-(21x+3)

determiningTheFunctionDomain
-(21x+3)+6

We get rid of parentheses

-21x-3+6

We add all the numbers together, and all the variables

-21x+3

Back to the equation:

-(-21x+3)


We get rid of parentheses

12x^2-4x+21x-3=0

We add all the numbers together, and all the variables

12x^2+17x-3=0

a = 12; b = 17; c = -3;
Δ = b2-4ac
Δ = 172-4·12·(-3)
Δ = 433
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-\sqrt{433}}{2*12}=\frac{-17-\sqrt{433}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{433}}{2*12}=\frac{-17+\sqrt{433}}{24}
$