-2(x-2)14x=3(x+1)-9x

Solution for -2(x-2)14x=3(x+1)-9x equation:

-2(x-2)14x=3(x+1)-9x

We move all terms to the left:

-2(x-2)14x-(3(x+1)-9x)=0

We multiply parentheses

-28x^2+56x-(3(x+1)-9x)=0


We calculate terms in parentheses: -(3(x+1)-9x), so:

3(x+1)-9x

We add all the numbers together, and all the variables

-9x+3(x+1)

We multiply parentheses

-9x+3x+3

We add all the numbers together, and all the variables

-6x+3

Back to the equation:

-(-6x+3)


We get rid of parentheses

-28x^2+56x+6x-3=0

We add all the numbers together, and all the variables

-28x^2+62x-3=0

a = -28; b = 62; c = -3;
Δ = b2-4ac
Δ = 622-4·(-28)·(-3)
Δ = 3508
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:

$\sqrt{\Delta}=\sqrt{3508}=\sqrt{4*877}=\sqrt{4}*\sqrt{877}=2\sqrt{877}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(62)-2\sqrt{877}}{2*-28}=\frac{-62-2\sqrt{877}}{-56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(62)+2\sqrt{877}}{2*-28}=\frac{-62+2\sqrt{877}}{-56}
$