2x(9x+6)=3(x-2)+4(2-3x)+1

Solution for 2x(9x+6)=3(x-2)+4(2-3x)+1 equation:

2x(9x+6)=3(x-2)+4(2-3x)+1

We move all terms to the left:

2x(9x+6)-(3(x-2)+4(2-3x)+1)=0

We add all the numbers together, and all the variables

2x(9x+6)-(3(x-2)+4(-3x+2)+1)=0

We multiply parentheses

18x^2+12x-(3(x-2)+4(-3x+2)+1)=0


We calculate terms in parentheses: -(3(x-2)+4(-3x+2)+1), so:

3(x-2)+4(-3x+2)+1

We multiply parentheses

3x-12x-6+8+1

We add all the numbers together, and all the variables

-9x+3

Back to the equation:

-(-9x+3)


We get rid of parentheses

18x^2+12x+9x-3=0

We add all the numbers together, and all the variables

18x^2+21x-3=0

a = 18; b = 21; c = -3;
Δ = b2-4ac
Δ = 212-4·18·(-3)
Δ = 657
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{657}=\sqrt{9*73}=\sqrt{9}*\sqrt{73}=3\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-3\sqrt{73}}{2*18}=\frac{-21-3\sqrt{73}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+3\sqrt{73}}{2*18}=\frac{-21+3\sqrt{73}}{36}
$