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

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

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

We move all terms to the left:

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

We get rid of parentheses

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


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

(4x+3)+2

We get rid of parentheses

4x+3+2

We add all the numbers together, and all the variables

4x+5

Back to the equation:

-(4x+5)


We get rid of parentheses

6x^2+2x-4x-5=0

We add all the numbers together, and all the variables

6x^2-2x-5=0

a = 6; b = -2; c = -5;
Δ = b2-4ac
Δ = -22-4·6·(-5)
Δ = 124
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:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{31}}{2*6}=\frac{2-2\sqrt{31}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{31}}{2*6}=\frac{2+2\sqrt{31}}{12}
$