6x(x+7)=3(2x+1)

Solution for 6x(x+7)=3(2x+1) equation:

6x(x+7)=3(2x+1)

We move all terms to the left:

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

We multiply parentheses

6x^2+42x-(3(2x+1))=0


We calculate terms in parentheses: -(3(2x+1)), so:

3(2x+1)

We multiply parentheses

6x+3

Back to the equation:

-(6x+3)


We get rid of parentheses

6x^2+42x-6x-3=0

We add all the numbers together, and all the variables

6x^2+36x-3=0

a = 6; b = 36; c = -3;
Δ = b2-4ac
Δ = 362-4·6·(-3)
Δ = 1368
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:

$\sqrt{\Delta}=\sqrt{1368}=\sqrt{36*38}=\sqrt{36}*\sqrt{38}=6\sqrt{38}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-6\sqrt{38}}{2*6}=\frac{-36-6\sqrt{38}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+6\sqrt{38}}{2*6}=\frac{-36+6\sqrt{38}}{12}
$