2x+3(x-4)=2(2x-6)x

Solution for 2x+3(x-4)=2(2x-6)x equation:

2x+3(x-4)=2(2x-6)x

We move all terms to the left:

2x+3(x-4)-(2(2x-6)x)=0

We multiply parentheses

2x+3x-(2(2x-6)x)-12=0


We calculate terms in parentheses: -(2(2x-6)x), so:

2(2x-6)x

We multiply parentheses

4x^2-12x

Back to the equation:

-(4x^2-12x)


We add all the numbers together, and all the variables

5x-(4x^2-12x)-12=0

We get rid of parentheses

-4x^2+5x+12x-12=0

We add all the numbers together, and all the variables

-4x^2+17x-12=0

a = -4; b = 17; c = -12;
Δ = b2-4ac
Δ = 172-4·(-4)·(-12)
Δ = 97
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{-(17)-\sqrt{97}}{2*-4}=\frac{-17-\sqrt{97}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{97}}{2*-4}=\frac{-17+\sqrt{97}}{-8}
$