3x(2x-1)=x+7(x+1)

Solution for 3x(2x-1)=x+7(x+1) equation:

3x(2x-1)=x+7(x+1)

We move all terms to the left:

3x(2x-1)-(x+7(x+1))=0

We multiply parentheses

6x^2-3x-(x+7(x+1))=0


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

x+7(x+1)

We multiply parentheses

x+7x+7

We add all the numbers together, and all the variables

8x+7

Back to the equation:

-(8x+7)


We get rid of parentheses

6x^2-3x-8x-7=0

We add all the numbers together, and all the variables

6x^2-11x-7=0

a = 6; b = -11; c = -7;
Δ = b2-4ac
Δ = -112-4·6·(-7)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-17}{2*6}=\frac{-6}{12}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+17}{2*6}=\frac{28}{12}
=2+1/3
$