2x(4x-1)=(x+5)(x+6)

Solution for 2x(4x-1)=(x+5)(x+6) equation:

2x(4x-1)=(x+5)(x+6)

We move all terms to the left:

2x(4x-1)-((x+5)(x+6))=0

We multiply parentheses

8x^2-2x-((x+5)(x+6))=0

We multiply parentheses ..

8x^2-((+x^2+6x+5x+30))-2x=0


We calculate terms in parentheses: -((+x^2+6x+5x+30)), so:

(+x^2+6x+5x+30)

We get rid of parentheses

x^2+6x+5x+30

We add all the numbers together, and all the variables

x^2+11x+30

Back to the equation:

-(x^2+11x+30)


We add all the numbers together, and all the variables

8x^2-2x-(x^2+11x+30)=0

We get rid of parentheses

8x^2-x^2-2x-11x-30=0

We add all the numbers together, and all the variables

7x^2-13x-30=0

a = 7; b = -13; c = -30;
Δ = b2-4ac
Δ = -132-4·7·(-30)
Δ = 1009
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{-(-13)-\sqrt{1009}}{2*7}=\frac{13-\sqrt{1009}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{1009}}{2*7}=\frac{13+\sqrt{1009}}{14}
$