2x(x-9)=3x(x+8)

Solution for 2x(x-9)=3x(x+8) equation:

2x(x-9)=3x(x+8)

We move all terms to the left:

2x(x-9)-(3x(x+8))=0

We multiply parentheses

2x^2-18x-(3x(x+8))=0


We calculate terms in parentheses: -(3x(x+8)), so:

3x(x+8)

We multiply parentheses

3x^2+24x

Back to the equation:

-(3x^2+24x)


We get rid of parentheses

2x^2-3x^2-18x-24x=0

We add all the numbers together, and all the variables

-1x^2-42x=0

a = -1; b = -42; c = 0;
Δ = b2-4ac
Δ = -422-4·(-1)·0
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-42}{2*-1}=\frac{0}{-2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+42}{2*-1}=\frac{84}{-2}
=-42
$