3x-3=(3/4)*(2x+12)

Solution for 3x-3=(3/4)*(2x+12) equation:

3x-3=(3/4)(2x+12)

We move all terms to the left:

3x-3-((3/4)(2x+12))=0


Domain of the equation: 4)(2x+12))!=0

x∈R


We add all the numbers together, and all the variables

3x-((+3/4)(2x+12))-3=0

We multiply parentheses ..

-((+6x^2+3/4*12))+3x-3=0

We multiply all the terms by the denominator


-((+6x^2+3+3x*4*12))-3*4*12))=0


We calculate terms in parentheses: -((+6x^2+3+3x*4*12)), so:

(+6x^2+3+3x*4*12)

We get rid of parentheses

6x^2+3x*4*12+3

Wy multiply elements

6x^2+144x*1+3

Wy multiply elements

6x^2+144x+3

Back to the equation:

-(6x^2+144x+3)


We add all the numbers together, and all the variables

-(6x^2+144x+3)=0

We get rid of parentheses

-6x^2-144x-3=0

a = -6; b = -144; c = -3;
Δ = b2-4ac
Δ = -1442-4·(-6)·(-3)
Δ = 20664
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:

$\sqrt{\Delta}=\sqrt{20664}=\sqrt{36*574}=\sqrt{36}*\sqrt{574}=6\sqrt{574}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-6\sqrt{574}}{2*-6}=\frac{144-6\sqrt{574}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+6\sqrt{574}}{2*-6}=\frac{144+6\sqrt{574}}{-12}
$