-3(-4x-2)=13.5x(x-6)

Solution for -3(-4x-2)=13.5x(x-6) equation:

-3(-4x-2)=13.5x(x-6)

We move all terms to the left:

-3(-4x-2)-(13.5x(x-6))=0

We multiply parentheses

12x-(13.5x(x-6))+6=0


We calculate terms in parentheses: -(13.5x(x-6)), so:

13.5x(x-6)

We multiply parentheses

13x^2-78x

Back to the equation:

-(13x^2-78x)


We get rid of parentheses

-13x^2+12x+78x+6=0

We add all the numbers together, and all the variables

-13x^2+90x+6=0

a = -13; b = 90; c = +6;
Δ = b2-4ac
Δ = 902-4·(-13)·6
Δ = 8412
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:

$\sqrt{\Delta}=\sqrt{8412}=\sqrt{4*2103}=\sqrt{4}*\sqrt{2103}=2\sqrt{2103}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-2\sqrt{2103}}{2*-13}=\frac{-90-2\sqrt{2103}}{-26}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+2\sqrt{2103}}{2*-13}=\frac{-90+2\sqrt{2103}}{-26}
$