3(x-4)=5(x+6)x=

Solution for 3(x-4)=5(x+6)x= equation:

3(x-4)=5(x+6)x=

We move all terms to the left:

3(x-4)-(5(x+6)x)=0

We multiply parentheses

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


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

5(x+6)x

We multiply parentheses

5x^2+30x

Back to the equation:

-(5x^2+30x)


We get rid of parentheses

-5x^2+3x-30x-12=0

We add all the numbers together, and all the variables

-5x^2-27x-12=0

a = -5; b = -27; c = -12;
Δ = b2-4ac
Δ = -272-4·(-5)·(-12)
Δ = 489
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{-(-27)-\sqrt{489}}{2*-5}=\frac{27-\sqrt{489}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{489}}{2*-5}=\frac{27+\sqrt{489}}{-10}
$