3(x+2)*4(2x)=6(x-7)

Solution for 3(x+2)*4(2x)=6(x-7) equation:

3(x+2)*4(2x)=6(x-7)

We move all terms to the left:

3(x+2)*4(2x)-(6(x-7))=0

We multiply parentheses

126x^2+252x-(6(x-7))=0


We calculate terms in parentheses: -(6(x-7)), so:

6(x-7)

We multiply parentheses

6x-42

Back to the equation:

-(6x-42)


We get rid of parentheses

126x^2+252x-6x+42=0

We add all the numbers together, and all the variables

126x^2+246x+42=0

a = 126; b = 246; c = +42;
Δ = b2-4ac
Δ = 2462-4·126·42
Δ = 39348
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:

$\sqrt{\Delta}=\sqrt{39348}=\sqrt{36*1093}=\sqrt{36}*\sqrt{1093}=6\sqrt{1093}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(246)-6\sqrt{1093}}{2*126}=\frac{-246-6\sqrt{1093}}{252}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(246)+6\sqrt{1093}}{2*126}=\frac{-246+6\sqrt{1093}}{252}
$