(6x+1)*x=(x+1)*(3x+8)

Solution for (6x+1)*x=(x+1)*(3x+8) equation:

(6x+1)*x=(x+1)(3x+8)

We move all terms to the left:

(6x+1)*x-((x+1)(3x+8))=0

We multiply parentheses

6x^2+x-((x+1)(3x+8))=0

We multiply parentheses ..

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


We calculate terms in parentheses: -((+3x^2+8x+3x+8)), so:

(+3x^2+8x+3x+8)

We get rid of parentheses

3x^2+8x+3x+8

We add all the numbers together, and all the variables

3x^2+11x+8

Back to the equation:

-(3x^2+11x+8)


We add all the numbers together, and all the variables

6x^2+x-(3x^2+11x+8)=0

We get rid of parentheses

6x^2-3x^2+x-11x-8=0

We add all the numbers together, and all the variables

3x^2-10x-8=0

a = 3; b = -10; c = -8;
Δ = b2-4ac
Δ = -102-4·3·(-8)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-14}{2*3}=\frac{-4}{6}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+14}{2*3}=\frac{24}{6}
=4
$