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

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

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

We move all terms to the left:

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

We multiply parentheses

6x^2-42x-((2x+1)(x-7))=0

We multiply parentheses ..

6x^2-((+2x^2-14x+x-7))-42x=0


We calculate terms in parentheses: -((+2x^2-14x+x-7)), so:

(+2x^2-14x+x-7)

We get rid of parentheses

2x^2-14x+x-7

We add all the numbers together, and all the variables

2x^2-13x-7

Back to the equation:

-(2x^2-13x-7)


We add all the numbers together, and all the variables

6x^2-42x-(2x^2-13x-7)=0

We get rid of parentheses

6x^2-2x^2-42x+13x+7=0

We add all the numbers together, and all the variables

4x^2-29x+7=0

a = 4; b = -29; c = +7;
Δ = b2-4ac
Δ = -292-4·4·7
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-27}{2*4}=\frac{2}{8}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+27}{2*4}=\frac{56}{8}
=7
$