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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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


We calculate terms in parentheses: -(7x(x+3)), so:

7x(x+3)

We multiply parentheses

7x^2+21x

Back to the equation:

-(7x^2+21x)


We add all the numbers together, and all the variables

7x-(7x^2+21x)-6=0

We get rid of parentheses

-7x^2+7x-21x-6=0

We add all the numbers together, and all the variables

-7x^2-14x-6=0

a = -7; b = -14; c = -6;
Δ = b2-4ac
Δ = -142-4·(-7)·(-6)
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{7}}{2*-7}=\frac{14-2\sqrt{7}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{7}}{2*-7}=\frac{14+2\sqrt{7}}{-14}
$