3x(2x+1)+2x=7x(3x-1)-84

Solution for 3x(2x+1)+2x=7x(3x-1)-84 equation:

3x(2x+1)+2x=7x(3x-1)-84

We move all terms to the left:

3x(2x+1)+2x-(7x(3x-1)-84)=0

We add all the numbers together, and all the variables

2x+3x(2x+1)-(7x(3x-1)-84)=0

We multiply parentheses

6x^2+2x+3x-(7x(3x-1)-84)=0


We calculate terms in parentheses: -(7x(3x-1)-84), so:

7x(3x-1)-84

We multiply parentheses

21x^2-7x-84

Back to the equation:

-(21x^2-7x-84)


We add all the numbers together, and all the variables

6x^2+5x-(21x^2-7x-84)=0

We get rid of parentheses

6x^2-21x^2+5x+7x+84=0

We add all the numbers together, and all the variables

-15x^2+12x+84=0

a = -15; b = 12; c = +84;
Δ = b2-4ac
Δ = 122-4·(-15)·84
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-72}{2*-15}=\frac{-84}{-30}
=2+4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+72}{2*-15}=\frac{60}{-30}
=-2
$