12x+8+2x=7x(2x+1)

Solution for 12x+8+2x=7x(2x+1) equation:

12x+8+2x=7x(2x+1)

We move all terms to the left:

12x+8+2x-(7x(2x+1))=0

We add all the numbers together, and all the variables

14x-(7x(2x+1))+8=0


We calculate terms in parentheses: -(7x(2x+1)), so:

7x(2x+1)

We multiply parentheses

14x^2+7x

Back to the equation:

-(14x^2+7x)


We get rid of parentheses

-14x^2+14x-7x+8=0

We add all the numbers together, and all the variables

-14x^2+7x+8=0

a = -14; b = 7; c = +8;
Δ = b2-4ac
Δ = 72-4·(-14)·8
Δ = 497
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{497}}{2*-14}=\frac{-7-\sqrt{497}}{-28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{497}}{2*-14}=\frac{-7+\sqrt{497}}{-28}
$