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

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

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

We move all terms to the left:

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


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

4x(x-6)

We multiply parentheses

4x^2-24x

Back to the equation:

-(4x^2-24x)


We get rid of parentheses

-4x^2-23x+24x+6=0

We add all the numbers together, and all the variables

-4x^2+x+6=0

a = -4; b = 1; c = +6;
Δ = b2-4ac
Δ = 12-4·(-4)·6
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{-(1)-\sqrt{97}}{2*-4}=\frac{-1-\sqrt{97}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{97}}{2*-4}=\frac{-1+\sqrt{97}}{-8}
$