15x+12+3x(2x-6)=3x-(21x-1)+2

Solution for 15x+12+3x(2x-6)=3x-(21x-1)+2 equation:

15x+12+3x(2x-6)=3x-(21x-1)+2

We move all terms to the left:

15x+12+3x(2x-6)-(3x-(21x-1)+2)=0

We multiply parentheses

6x^2+15x-18x-(3x-(21x-1)+2)+12=0


We calculate terms in parentheses: -(3x-(21x-1)+2), so:

3x-(21x-1)+2

We get rid of parentheses

3x-21x+1+2

We add all the numbers together, and all the variables

-18x+3

Back to the equation:

-(-18x+3)


We add all the numbers together, and all the variables

6x^2-3x-(-18x+3)+12=0

We get rid of parentheses

6x^2-3x+18x-3+12=0

We add all the numbers together, and all the variables

6x^2+15x+9=0

a = 6; b = 15; c = +9;
Δ = b2-4ac
Δ = 152-4·6·9
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3}{2*6}=\frac{-18}{12}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3}{2*6}=\frac{-12}{12}
=-1
$