6x(x+7)=x+47

Solution for 6x(x+7)=x+47 equation:

6x(x+7)=x+47

We move all terms to the left:

6x(x+7)-(x+47)=0

We multiply parentheses

6x^2+42x-(x+47)=0

We get rid of parentheses

6x^2+42x-x-47=0

We add all the numbers together, and all the variables

6x^2+41x-47=0

a = 6; b = 41; c = -47;
Δ = b2-4ac
Δ = 412-4·6·(-47)
Δ = 2809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2809}=53$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(41)-53}{2*6}=\frac{-94}{12}
=-7+5/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+53}{2*6}=\frac{12}{12}
=1
$