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

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

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

We move all terms to the left:

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

determiningTheFunctionDomain
-(1-32x^2)-6x(x+3)+4=0

We multiply parentheses

-(1-32x^2)-6x^2-18x+4=0

We get rid of parentheses

32x^2-6x^2-18x-1+4=0

We add all the numbers together, and all the variables

26x^2-18x+3=0

a = 26; b = -18; c = +3;
Δ = b2-4ac
Δ = -182-4·26·3
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{3}}{2*26}=\frac{18-2\sqrt{3}}{52}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{3}}{2*26}=\frac{18+2\sqrt{3}}{52}
$