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

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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 $

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