2(x-7)=3x(9+x)

Solution for 2(x-7)=3x(9+x) equation:

2(x-7)=3x(9+x)

We move all terms to the left:

2(x-7)-(3x(9+x))=0

We add all the numbers together, and all the variables

2(x-7)-(3x(x+9))=0

We multiply parentheses

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


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

3x(x+9)

We multiply parentheses

3x^2+27x

Back to the equation:

-(3x^2+27x)


We get rid of parentheses

-3x^2+2x-27x-14=0

We add all the numbers together, and all the variables

-3x^2-25x-14=0

a = -3; b = -25; c = -14;
Δ = b2-4ac
Δ = -252-4·(-3)·(-14)
Δ = 457
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{-(-25)-\sqrt{457}}{2*-3}=\frac{25-\sqrt{457}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+\sqrt{457}}{2*-3}=\frac{25+\sqrt{457}}{-6}
$