2x(x+6)+x=3x+8

Solution for 2x(x+6)+x=3x+8 equation:

2x(x+6)+x=3x+8

We move all terms to the left:

2x(x+6)+x-(3x+8)=0

We add all the numbers together, and all the variables

x+2x(x+6)-(3x+8)=0

We multiply parentheses

2x^2+x+12x-(3x+8)=0

We get rid of parentheses

2x^2+x+12x-3x-8=0

We add all the numbers together, and all the variables

2x^2+10x-8=0

a = 2; b = 10; c = -8;
Δ = b2-4ac
Δ = 102-4·2·(-8)
Δ = 164
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:

$\sqrt{\Delta}=\sqrt{164}=\sqrt{4*41}=\sqrt{4}*\sqrt{41}=2\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{41}}{2*2}=\frac{-10-2\sqrt{41}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{41}}{2*2}=\frac{-10+2\sqrt{41}}{4}
$