3(x-2)=-4(4+3x)15x

Solution for 3(x-2)=-4(4+3x)15x equation:

3(x-2)=-4(4+3x)15x

We move all terms to the left:

3(x-2)-(-4(4+3x)15x)=0

We add all the numbers together, and all the variables

3(x-2)-(-4(3x+4)15x)=0

We multiply parentheses

3x-(-4(3x+4)15x)-6=0


We calculate terms in parentheses: -(-4(3x+4)15x), so:

-4(3x+4)15x

We multiply parentheses

-180x^2-240x

Back to the equation:

-(-180x^2-240x)


We get rid of parentheses

180x^2+240x+3x-6=0

We add all the numbers together, and all the variables

180x^2+243x-6=0

a = 180; b = 243; c = -6;
Δ = b2-4ac
Δ = 2432-4·180·(-6)
Δ = 63369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{63369}=\sqrt{9*7041}=\sqrt{9}*\sqrt{7041}=3\sqrt{7041}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(243)-3\sqrt{7041}}{2*180}=\frac{-243-3\sqrt{7041}}{360}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(243)+3\sqrt{7041}}{2*180}=\frac{-243+3\sqrt{7041}}{360}
$