6x(2x-5)=6(x-4)+9

Solution for 6x(2x-5)=6(x-4)+9 equation:

6x(2x-5)=6(x-4)+9

We move all terms to the left:

6x(2x-5)-(6(x-4)+9)=0

We multiply parentheses

12x^2-30x-(6(x-4)+9)=0


We calculate terms in parentheses: -(6(x-4)+9), so:

6(x-4)+9

We multiply parentheses

6x-24+9

We add all the numbers together, and all the variables

6x-15

Back to the equation:

-(6x-15)


We get rid of parentheses

12x^2-30x-6x+15=0

We add all the numbers together, and all the variables

12x^2-36x+15=0

a = 12; b = -36; c = +15;
Δ = b2-4ac
Δ = -362-4·12·15
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-24}{2*12}=\frac{12}{24}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+24}{2*12}=\frac{60}{24}
=2+1/2
$