2x=(2x+5)*(x-6)

Solution for 2x=(2x+5)*(x-6) equation:

2x=(2x+5)(x-6)

We move all terms to the left:

2x-((2x+5)(x-6))=0

We multiply parentheses ..

-((+2x^2-12x+5x-30))+2x=0


We calculate terms in parentheses: -((+2x^2-12x+5x-30)), so:

(+2x^2-12x+5x-30)

We get rid of parentheses

2x^2-12x+5x-30

We add all the numbers together, and all the variables

2x^2-7x-30

Back to the equation:

-(2x^2-7x-30)


We add all the numbers together, and all the variables

2x-(2x^2-7x-30)=0

We get rid of parentheses

-2x^2+2x+7x+30=0

We add all the numbers together, and all the variables

-2x^2+9x+30=0

a = -2; b = 9; c = +30;
Δ = b2-4ac
Δ = 92-4·(-2)·30
Δ = 321
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{-(9)-\sqrt{321}}{2*-2}=\frac{-9-\sqrt{321}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{321}}{2*-2}=\frac{-9+\sqrt{321}}{-4}
$