2x=(3x+6)(3x-10)

Solution for 2x=(3x+6)(3x-10) equation:

2x=(3x+6)(3x-10)

We move all terms to the left:

2x-((3x+6)(3x-10))=0

We multiply parentheses ..

-((+9x^2-30x+18x-60))+2x=0


We calculate terms in parentheses: -((+9x^2-30x+18x-60)), so:

(+9x^2-30x+18x-60)

We get rid of parentheses

9x^2-30x+18x-60

We add all the numbers together, and all the variables

9x^2-12x-60

Back to the equation:

-(9x^2-12x-60)


We add all the numbers together, and all the variables

2x-(9x^2-12x-60)=0

We get rid of parentheses

-9x^2+2x+12x+60=0

We add all the numbers together, and all the variables

-9x^2+14x+60=0

a = -9; b = 14; c = +60;
Δ = b2-4ac
Δ = 142-4·(-9)·60
Δ = 2356
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:

$\sqrt{\Delta}=\sqrt{2356}=\sqrt{4*589}=\sqrt{4}*\sqrt{589}=2\sqrt{589}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{589}}{2*-9}=\frac{-14-2\sqrt{589}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{589}}{2*-9}=\frac{-14+2\sqrt{589}}{-18}
$