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

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

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

We move all terms to the left:

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

We multiply parentheses

-21x^2-42x-(-3(2x-3)+x)=0


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

-3(2x-3)+x

We add all the numbers together, and all the variables

x-3(2x-3)

We multiply parentheses

x-6x+9

We add all the numbers together, and all the variables

-5x+9

Back to the equation:

-(-5x+9)


We get rid of parentheses

-21x^2-42x+5x-9=0

We add all the numbers together, and all the variables

-21x^2-37x-9=0

a = -21; b = -37; c = -9;
Δ = b2-4ac
Δ = -372-4·(-21)·(-9)
Δ = 613
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{-(-37)-\sqrt{613}}{2*-21}=\frac{37-\sqrt{613}}{-42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+\sqrt{613}}{2*-21}=\frac{37+\sqrt{613}}{-42}
$