2(3x-12)-5x=-3x(x-12)

Solution for 2(3x-12)-5x=-3x(x-12) equation:

2(3x-12)-5x=-3x(x-12)

We move all terms to the left:

2(3x-12)-5x-(-3x(x-12))=0

We add all the numbers together, and all the variables

-5x+2(3x-12)-(-3x(x-12))=0

We multiply parentheses

-5x+6x-(-3x(x-12))-24=0


We calculate terms in parentheses: -(-3x(x-12)), so:

-3x(x-12)

We multiply parentheses

-3x^2+36x

Back to the equation:

-(-3x^2+36x)


We add all the numbers together, and all the variables

-(-3x^2+36x)+x-24=0

We get rid of parentheses

3x^2-36x+x-24=0

We add all the numbers together, and all the variables

3x^2-35x-24=0

a = 3; b = -35; c = -24;
Δ = b2-4ac
Δ = -352-4·3·(-24)
Δ = 1513
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{-(-35)-\sqrt{1513}}{2*3}=\frac{35-\sqrt{1513}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+\sqrt{1513}}{2*3}=\frac{35+\sqrt{1513}}{6}
$