2(x+1)-3(4x2)=6x

Solution for 2(x+1)-3(4x2)=6x equation:

2(x+1)-3(4x^2)=6x

We move all terms to the left:

2(x+1)-3(4x^2)-(6x)=0

determiningTheFunctionDomain
-34x^2+2(x+1)-6x=0

We add all the numbers together, and all the variables

-34x^2-6x+2(x+1)=0

We multiply parentheses

-34x^2-6x+2x+2=0

We add all the numbers together, and all the variables

-34x^2-4x+2=0

a = -34; b = -4; c = +2;
Δ = b2-4ac
Δ = -42-4·(-34)·2
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-12\sqrt{2}}{2*-34}=\frac{4-12\sqrt{2}}{-68}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+12\sqrt{2}}{2*-34}=\frac{4+12\sqrt{2}}{-68}
$